# Featured Research

## EXPLORE IDM’S CURRENT RESEARCH GROUPS

The research and modeling team at IDM is focused on providing support to disease eradication programs and other global health endeavors through a variety of modeling and statistical approaches. We build mechanistic agent-based models in order to understand model assumptions and input data, examine the effects of population-level and within-host phenomena, and stimulate the impact of combined interventions, especially for all phases of an eradication effort.

The Computational Science Research (CSR) team develops algorithmic tools to increase the capability, usability, and efficiency of modeling methodology in support of stakeholders at IDM and partner organizations. CSR conducts novel and translational research to support the use of data and models in making better decisions regarding health and development. In addition to algorithm development, we support application and refinement of these methods in partnership with programmatic teams within IDM and beyond. Key initiatives within CSR include the following:

• Calibration - propagating structural and parametric uncertainty when fitting stochastic models like EMOD to historical data.
• Optimization - local and global numerical methods to find the best parameters or mix of interventions.
• Exploration - efficiently find interesting regions of parameter space.
• Design - efficiently use super-computing resources to achieve a simulation-based objective.
• AI-based approaches to health and development planning under uncertainty, with a focus on the value of information.

Atiye Alaeddini, Kristi A.Morgansen, Mehran Mesbahi

Systems &amp; Control Letters

This paper is concerned with the design of an augmented state feedback controller for finite-dimensional linear systems with nonlinear observation dynamics. Most of the theoretical results in the area of (optimal) feedback design are based on the assumption that the state is available for measurement. In this paper, we focus on finding a feedback control that avoids state trajectories with undesirable observability properties. In particular, we introduce an optimal control problem that specifically considers an index of observability in the control synthesis. The resulting cost functional is a combination of LQR-like quadratic terms and an index of observability. The main contribution of the paper is presenting a control synthesis procedure that on one hand, provides closed loop asymptotic stability, and addresses the observability of the system – as a transient performance criterion – on the other.

Bulletin of Mathematical Biology

As mathematical models and computational tools become more sophisticated and powerful to accurately depict system dynamics, numerical methods that were previously considered computationally impractical started being utilized for large-scale simulations. Methods that characterize a rare event in biochemical systems are part of such phenomenon, as many of them are computationally expensive and require high-performance computing. In this paper, we introduce an enhanced version of the doubly weighted stochastic simulation algorithm (dwSSA) (Daigle et al. in J Chem Phys 134:044110, 2011), called dwSSA++, that significantly improves the speed of convergence to the rare event of interest when the conventional multilevel cross-entropy method in dwSSA is either unable to converge or converges very slowly. This achievement is enabled by a novel polynomial leaping method that uses past data to detect slow convergence and attempts to push the system toward the rare event. We demonstrate the performance of dwSSA++ on two systems—a susceptible–infectious–recovered–susceptible disease dynamics model and a yeast polarization model—and compare its computational efficiency to that of dwSSA.

Atiye Alaeddini, Siavash Alemzadeh, Afshin Mesbahi, and Mehran Mesbahi

arXiv preprint arXiv:1807.06611

Data-driven methods for modeling dynamic systems have recently received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series had been generated, regression on the system model has been particularly popular. In the linear case, the resulting least squares setup for model regression, not only provides a computationally viable method to fit a model to the data, but also provides useful insights into the modal properties of the underlying dynamics. Although probabilistic estimates for this model regression have been reported, deterministic error bounds have not been examined in the literature, particularly as they pertain to the properties of the underlying system. In this paper, we provide deterministic non-asymptotic error bounds for fitting a linear model to observed time-series data, with a particular attention to the role of symmetry and eigenvalue multiplicity in the underlying system matrix.

Isobel Routledge, José Eduardo Romero Chevéz, Zulma M. Cucunubá, Manuel Gomez Rodriguez, Caterina Guinovart, Kyle B Gustafson,  Kammerle Schneider, Patrick G.T. Walker, Azra C. Ghani, Samir Bhatt

Nature Communications

In 2016 the World Health Organization identified 21 countries that could eliminate malaria by 2020. Monitoring progress towards this goal requires tracking ongoing transmission. Here we develop methods that estimate individual reproduction numbers and their variation through time and space. Individual reproduction numbers, Rc, describe the state of transmission at a point in time and differ from mean reproduction numbers, which are averages of the number of people infected by a typical case. We assess elimination progress in El Salvador using data for confirmed cases of malaria from 2010 to 2016. Our results demonstrate that whilst the average number of secondary malaria cases was below one (0.61, 95% CI 0.55–0.65), individual reproduction numbers often exceeded one. We estimate a decline in Rc between 2010 and 2016. However we also show that if importation is maintained at the same rate, the country may not achieve malaria elimination by 2020.

Joshua Proctor , Kyle B. Gustafson, Joshua L. Proctor

arXiv.org q-bio

Containing the recent West African outbreak of Ebola virus (EBOV) required the deployment of substantial global resources. Operationally, health workers and surveillance teams treated cases, collected genetic samples, and tracked case contacts. Despite the substantial progress in analyzing and modeling EBOV epidemiological data, a complete characterization of the spatiotemporal spread of Ebola cases remains a challenge. In this work, we offer a novel perspective on the EBOV epidemic that utilizes virus genome sequences to inform population-level, spatial models. Calibrated to phylogenetic linkages, these dynamic spatial models provide unique insight into the disease mobility of EBOV in Sierra Leone. Further, we developed a model selection framework that identifies important epidemiological variables influencing the spatiotemporal propagation of EBOV. Consistent with other investigations, our results show that the spread of EBOV during the beginning and middle portions of the epidemic strongly depended on the size of and distance between populations. Our analysis also revealed a substantial decline in the dependence on population size at the end of the epidemic, coinciding with the large-scale intervention campaign: Operation Western Area Surge. More generally, we believe this framework, pairing molecular diagnostics with dynamic models, has the potential to be a powerful forecasting tool along with offering operationally-relevant guidance for surveillance and sampling strategies during an epidemic.

Daniel Klein , Atiye Alaeddini, and Daniel J Klein

Proceedings of the 2017 Winter Simulation Conference

### Introduction

In public health, it is critical to have a reasonable understanding of an epidemic disease in order to set pragmatic goals and design highly-impactful and cost-effective interventions. Mathematical models of these epidemiological processes can support decision making by forecasting disease spread in space and time, and by evaluating intervention outcomes many times in-silico before spending valuable resources implementing real-world programs. Recent efforts in computational epidemiology have focused on the design and application of detailed stochastic models that capture physical mechanisms through which disease propagates, along with the statistical fluctuations inherent in complex systems. These stochastic models are readily available, and recent work has focused on applying these models to malaria (Eckhoff et al. 2016, Eckhoff 2013, Marshall et al. 2016, Gerardin et al. 2016), HIV (Bershteyn et al. 2016, Eaton et al. 2015), polio (McCarthy et al. 2016, Grassly et al. 2006), and more.

### Simulation

Some types of diseases with permanent immunity, such as measles, mumps and rubella, can be described as Susceptible-Infected-Recovered (SIR) model. In this model each individual can only exist in one of the discrete states such as susceptible (S), infected (I) or permanently recovered (R). We have two transitions in this case. An infected person can infect others with an infection rate, β, and is cured with curing rate, δ. Therefore, the parameters of our model are θ = (β,δ). Our objective, here, is finding a good model for the given epidemic data, i.e. infection rate and curing rate, to investigate the properties of the disease spread. These properties will allow the researchers to learn about the diseases, and thereby enabling them to test competing theories about transmission of disease and to devise better containment strategies.

Neil Sherborne, Joel C. Miller, Konstantin B. Blyuss, Istvan Z. Kiss

Journal of Mathematical Biology

This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes. This implies that the new model is exact on the ensemble of configuration model networks of infinite size. For the case of Markovian transmission the message passing model is re-parametrised into a pairwise-like model which is then used to derive many well-known pairwise models for regular networks, or when the infectious period is exponentially distributed or is of a fixed length.

Kyle Gustafson, Basil Bayati, Philip Welkhoff

Fractional Diffusion Emulates a Human Mobility Network during a Simulated Disease Outbreak

Mobility networks facilitate the growth of populations, the success of invasive species, and the spread of communicable diseases among social animals, including humans.Disease control and elimination efforts, especially during an outbreak, can be optimized by numerical modeling of disease dynamics on transport networks. This is especially true when incidence data from an emerging epidemic is sparse and unreliable. However, mobility networks can be complex, challenging to characterize, and expensive to simulate with agent-based models. We therefore studied a parsimonious model for spatiotemporal disease dynamics based on a fractional diffusion equation. We implemented new stochastic simulations of a prototypical influenza-like infection spreading through the United States’ highly-connected air travel network. We found that the national-averaged infected fraction during an outbreak is accurately reproduced by a space-fractional diffusion equation consistent with the connectivity of airports. Fractional diffusion therefore seems to be a better model of network outbreak dynamics than a diffusive model. Our fractional reaction-diffusion method and the result could be extended to other mobility networks in a variety of applications for population dynamics.

Atiye Alaeddini, Kristi A. Morgansen, Mehran Mesbahi

2017 American Control Conference (ACC)

Utilizing the concept of observability, in conjunction with tools from graph theory and optimization, this paper develops an algorithm for network synthesis with privacy guarantees. In particular, we propose an algorithm for the selection of optimal weights for the communication graph in order to maximize the privacy of nodes in the network, from a control theoretic perspective. In this direction, we propose an observability-based design of the communication topology that improves the privacy of the network in presence of an intruder. The resulting adaptive network responds to the intrusion by changing the topology of the network-in an online manner- in order to reduce the information exposed to the intruder.

Infectious Disease Modeling

The emergence of Zika and Ebola demonstrates the importance of understanding the role of sexual transmission in the spread of diseases with a primarily non-sexual transmission route. In this paper, we develop low-dimensional models for how an SIR disease will spread if it transmits through a sexual contact network and some other transmission mechanism, such as direct contact or vectors. We show that the models derived accurately predict the dynamics of simulations in the large population limit, and investigate ℛ0 and final size relations.

Min K. Roh & Bernie J. Daigle Jr.

BMC Systems Biology

Background
Despite the increasing availability of high performance computing capabilities, analysis and characterization of stochastic biochemical systems remain a computational challenge. To address this challenge, the Stochastic Parameter Search for Events (SParSE) was developed to automatically identify reaction rates that yield a probabilistic user-specified event. SParSE consists of three main components: the multi-level cross-entropy method, which identifies biasing parameters to push the system toward the event of interest, the related inverse biasing method, and an optional interpolation of identified parameters. While effective for many examples, SParSE depends on the existence of a sufficient amount of intrinsic stochasticity in the system of interest. In the absence of this stochasticity, SParSE can either converge slowly or not at all.

Results
We have developed SParSE++, a substantially improved algorithm for characterizing target events in terms of system parameters. SParSE++ makes use of a series of novel parameter leaping methods that accelerate the convergence rate to the target event, particularly in low stochasticity cases. In addition, the interpolation stage is modified to compute multiple interpolants and to choose the optimal one in a statistically rigorous manner. We demonstrate the performance of SParSE++ on four example systems: a birth-death process, a reversible isomerization model, SIRS disease dynamics, and a yeast polarization model. In all four cases, SParSE++ shows significantly improved computational efficiency over SParSE, with the largest improvements resulting from analyses with the strictest error tolerances.

Conclusions
As researchers continue to model realistic biochemical systems, the need for efficient methods to characterize target events will grow. The algorithmic advancements provided by SParSE++ fulfill this need, enabling characterization of computationally intensive biochemical events that are currently resistant to analysis.

Physical Review E

In recent years, many variants of percolation have been used to study network structure and the behavior of processes spreading on networks. These include bond percolation, site percolation, k-core percolation, bootstrap percolation, the generalized epidemic process, and the Watts threshold model (WTM). We show that—except for bond percolation—each of these processes arises as a special case of the WTM, and bond percolation arises from a small modification. In fact “heterogeneous k-core percolation,” a corresponding “heterogeneous bootstrap percolation” model, and the generalized epidemic process are completely equivalent to one another and the WTM. We further show that a natural generalization of the WTM in which individuals “transmit” or “send a message” to their neighbors with some probability less than 1 can be reformulated in terms of the WTM, and so this apparent generalization is in fact not more general. Finally, we show that in bond percolation, finding the set of nodes in the component containing a given node is equivalent to finding the set of nodes activated if that node is initially activated and the node thresholds are chosen from the appropriate distribution. A consequence of these results is that mathematical techniques developed for the WTM apply to these other models as well, and techniques that were developed for some particular case may in fact apply much more generally.

Atiye Alaeddini, Kristi A. Morgansen

American Control Conference (ACC)

Given a network, we would like to determine which subset of nodes should be measured by limited sensing facilities to maximize information about the entire network. The optimal choice corresponds to the configuration that returns the highest value of a measure of observability of the system. Here, the determinant of the inverse of the observability Gramian is used to evaluate the degree of observability. Additionally, the effects of changes in the topology of the corresponding graph of a network on the observability of the network are investigated. The theory is illustrated on the problem of detection of an epidemic disease in a community. The purpose here is to find the smallest number of people who must be examined to predict the number of infected people in an arbitrary community. Results are demonstrated in simulation.

Physical Review E

We couple a stochastic collocation method with an analytical expansion of the canonical epidemiological master equation to analyze the effects of both extrinsic and intrinsic noise. It is shown that depending on the distribution of the extrinsic noise, the master equation yields quantitatively different results compared to using the expectation of the distribution for the stochastic parameter. This difference is incident to the nonlinear terms in the master equation, and we show that the deviation away from the expectation of the extrinsic noise scales nonlinearly with the variance of the distribution. The method presented here converges linearly with respect to the number of particles in the system and exponentially with respect to the order of the polynomials used in the stochastic collocation calculation. This makes the method presented here more accurate than standard Monte Carlo methods, which suffer from slow, nonmonotonic convergence. In epidemiological terms, the results show that extrinsic fluctuations should be taken into account since they effect the speed of disease breakouts and that the gamma distribution should be used to model the basic reproductive number.

Kyle B. Gustafson, Basil S. Bayati, Philip A. Eckhoff

arXiv.org, Cornell University Library

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between contact nodes. In some cases, transport can be parameterized with gravity-type models or approximated by a diffusive random walk. As a alternative, we have isolated intranational commercial air traffic as a case study for the utility of non-diffusive, heavy-tailed transport models. We implemented new stochastic simulations of a prototypical influenza-like infection, focusing on the dense, highly-connected United States air travel network. We show that mobility on this network can be described mainly by a power law, in agreement with previous studies. Remarkably, we find that the global evolution of an outbreak on this network is accurately reproduced by a two-parameter space-fractional diffusion equation, such that those parameters are determined by the air travel network.

arXiv.org, Cornell University Library

A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is derived and approximated in the frequency domain. The distribution for the final time is transformed back to the real domain and can be sampled from in a simulation. The result is an approximation of the classical stochastic simulation algorithm that requires fewer random variates. An analysis of the error and speedup compared to the stochastic simulation algorithm is presented.

Joshua Proctor , Joshua Proctor, S. L. Brunton, B. W. Brunton, J. N. Kutz

EPJ

Complex systems exhibit dynamics that typically evolve on low-dimensional attractors and may have sparse representation in some optimal basis. Recently developed compressive sensing techniques exploit this sparsity for state reconstruction and/or categorical identification from limited measurements. We argue that data-driven dimensionality reduction methods integrate naturally with sparse sensing in the context of complex systems. This framework works equally well with a physical model or in an equation-free context, where data is available but the governing equations may be unknown. We demonstrate the advantages of combining these methods on three prototypical examples: classification of dynamical regimes, optimal sensor placement, and equation-free dynamic model reduction. These examples motivate the potentially transformative role that state-of-the-art data methods and machine learning can play in the analysis of complex systems.

Min K Roh and Philip Eckhoff

BMC Systems Biology

### Background

With recent increase in affordability and accessibility of high-performance computing (HPC), the use of large stochastic models has become increasingly popular for its ability to accurately mimic the behavior of the represented biochemical system. One important application of such models is to predict parameter configurations that yield an event of scientific significance. Due to the high computational requirements of Monte Carlo simulations and dimensionality of parameter space, brute force search is computationally infeasible for most large models.

### Results

We have developed a novel parameter estimation algorithm—Stochastic Parameter Search for Events (SParSE)—that automatically computes parameter configurations for propagating the system to produce an event of interest at a user-specified success rate and error tolerance. Our method is highly automated and parallelizable. In addition, computational complexity does not scale linearly with the number of unknown parameters; all reaction rate parameters are updated concurrently at the end of each iteration in SParSE. We apply SParSE to three systems of increasing complexity: birth-death, reversible isomerization, and Susceptible-Infectious-Recovered-Susceptible (SIRS) disease transmission. Our results demonstrate that SParSE substantially accelerates computation of the parametric solution hyperplane compared to uniform random search. We also show that the novel heuristic for handling over-perturbing parameter sets enables SParSE to compute biasing parameters for a class of rare events that is not amenable to current algorithms that are based on importance sampling.

### Conclusions

SParSE provides a novel, efficient, event-oriented parameter estimation method for computing parametric configurations that can be readily applied to any stochastic systems obeying chemical master equation (CME). Its usability and utility do not diminish with large systems as the algorithmic complexity for a given system is independent of the number of unknown reaction rate parameters.

Daniel Klein , Daniel J. Klein, Michael Baym, and Philip Eckhoff

PLoS ONE

Decision makers in epidemiology and other disciplines are faced with the daunting challenge of designing interventions that will be successful with high probability and robust against a multitude of uncertainties. To facilitate the decision making process in the context of a goal-oriented objective (e.g., eradicate polio by ), stochastic models can be used to map the probability of achieving the goal as a function of parameters. Each run of a stochastic model can be viewed as a Bernoulli trial in which “success” is returned if and only if the goal is achieved in simulation. However, each run can take a significant amount of time to complete, and many replicates are required to characterize each point in parameter space, so specialized algorithms are required to locate desirable interventions.

Joshua Proctor , B. W. Brunton, S. L. Brunton, J. L. Proctor, J. N. Kutz

arXiv.org, Cornell University Library

The algorithm solves an l1-minimization to find the fewest entries of the full measurement vector that exactly reconstruct the discriminant vector in feature space. Once the sensor locations have been identified from the training data, subsequent test samples are classified with remarkable efficiency, achieving performance comparable to that obtained by discrimination using the full image. Sensor locations may be learned from full images, or from a random subsample of pixels. For classification between more than two categories, we introduce a coupling parameter whose value tunes the number of sensors selected, trading accuracy for economy. We demonstrate the algorithm on example datasets from image recognition using PCA for feature extraction and LDA for discrimination; however, the method can be broadly applied to non-image data and adapted to work with other methods for feature extraction and discrimination.

Hao Hu, Karima Nigmatulina, and Philip Eckhoff

Mathematical Biosciences

Contact rates and patterns among individuals in a geographic area drive transmission of directly-transmitted pathogens, making it essential to understand and estimate contacts for simulation of disease dynamics. Under the uniform mixing assumption, one of two mechanisms is typically used to describe the relation between contact rate and population density: density-dependent or frequency-dependent.  Based on existing evidence of population threshold and human mobility patterns, we formulated a spatial contact model to describe the appropriate form of transmission with initial growth at low density and saturation at higher density.  We show that the two mechanisms are extreme cases that do not capture real population movement across all scales.  Empirical data of human and wildlife diseases indicate that a nonlinear function may work better when looking at the full spectrum of densities. This estimation can be applied to large areas with population mixing in general activities.  For crowds with unusually large densities (e.g., transportation terminals, stadiums, or mass gatherings), the lack of organized social contact structure deviates the physical contacts towards a special case of the spatial contact model – the dynamics of kinetic gas molecule collision.  In this case, an ideal gas model with van der Waals correction fits well; existing movement observation data and the contact rate between individuals is estimated using kinetic theory.  A complete picture of contact rate scaling with population density may help clarify the definition of transmission rates in heterogeneous, large-scale spatial systems.

The Journal of Chemical Physics

A novel method is presented for the simulation of a discrete state space, continuous time Markov process subject to fractional diffusion. The method is based on Lie-Trotter operator splitting of the diffusion and reaction terms in the master equation. The diffusion term follows a multinomial distribution governed by a kernel that is the discretized solution of the fractional diffusion equation. The algorithm is validated and simulations are provided for the Fisher-KPP wavefront. It is shown that the wave speed is dictated by the order of the fractional derivative, where lower values result in a faster wave than in the case of classical diffusion. Since many physical processes deviate from classical diffusion, fractional diffusion methods are necessary for accurate simulations.

Basil S. Bayati and Philip A.Eckhoff

Physical Review E

We perform a high-order analytical expansion of the epidemiological susceptible-infectious-recovered multivariate master equation and include terms up to and beyond single-particle fluctuations. It is shown that higher order approximations yield qualitatively different results than low-order approximations, which is incident to the influence of additional nonlinear fluctuations. The fluctuations can be related to a meaningful physical parameter, the basic reproductive number, which is shown to dictate the rate of divergence in absolute terms from the ordinary differential equations more so than the total number of persons in the system. In epidemiological terms, the effect of single-particle fluctuations ought to be taken into account as the reproductive number approaches unity.

The Data, Dynamics, and Analytics (DDA) team is focused on applying modern data science, machine-learning, and statistical techniques to a wide-range of data including infectious disease data, household survey data, and genomic surveillance data. We aim to leverage the growing success of modern analytic and numerical methods as well as developing new mathematical methodologies tailored to the types of data being collected in resource-constrained settings. The primary goal is to help with near-term public policy questions facing the global health community.
Some areas of interest include:

• Collaborating with IDM disease teams to enable the usage of advanced analytic and numerical techniques;
• Investigating genomic and other molecular surveillance data to inform decisions on intervention and elimination strategies;
• Developing new mathematical techniques to analyze high-dimensional, timeseries data to construct models and forecast;
• Integrating geospatial data into mechanistic and equation-free dynamic modeling;
• Incorporating small area estimation methodologies with complex survey data for Family Planning indicators in resource-constrained settings.

Dennis Chao , Joshua Proctor , Ben J Brintz, Benjamin Haaland, Joel Howard, Dennis L Chao, Joshua L Proctor, Ashraful I Khan, Sharia M Ahmed, Lindsay T Keegan, Tom Greene

eLife

Traditional clinical prediction models focus on parameters of the individual patient. For infectious diseases, sources external to the patient, including characteristics of prior patients and seasonal factors, may improve predictive performance. We describe the development of a predictive model that integrates multiple sources of data in a principled statistical framework using a post-test odds formulation. Our method enables electronic real-time updating and flexibility, such that components can be included or excluded according to data availability. We apply this method to the prediction of etiology of pediatric diarrhea, where 'pre-test’ epidemiologic data may be highly informative. Diarrhea has a high burden in low-resource settings, and antibiotics are often over-prescribed. We demonstrate that our integrative method outperforms traditional prediction in accurately identifying cases with a viral etiology, and show that its clinical application, especially when used with an additional diagnostic test, could result in a 61% reduction in inappropriately prescribed antibiotics.

Navideh Noori , Mollie Van Gordon , Brittany Hagedorn , Ben Althouse , Edward Wenger , Andre Lin Ouedraogo , Laura Skrip, Karim Derra, Mikaila Kaboré, Navideh Noori, Adama Gansané, Innocent Valéa, Halidou Tinto, Bicaba W. Brice, Mollie Van Gordon, Brittany Hagedorn, Hervé Hien, Benjamin M. Althouse, Edward A. Wenger, André Lin Ouédraogo

International Journal of Infectious Diseases

### Background

Absolute numbers of COVID-19 cases and deaths reported to date in the sub-Saharan Africa (SSA) region have been significantly lower than those across the Americas, Asia, and Europe. As a result, there has been limited information about the demographic and clinical characteristics of deceased cases in the region, as well as the impacts of different case management strategies.

### Methods

Data from deceased cases reported across SSA through May 10, 2020 and from hospitalized cases in Burkina Faso through April 15, 2020 were analyzed. Demographic, epidemiological, and clinical information on deceased cases in SSA was derived through a line-list of publicly available information and, for cases in Burkina Faso, from aggregate records at the Centre Hospitalier Universitaire de Tengandogo in Ouagadougou. A synthetic case population was derived probabilistically using distributions of age, sex, and underlying conditions from populations of West African countries to assess individual risk factors and treatment effect sizes. Logistic regression analysis was conducted to evaluate the adjusted odds of survival for patients receiving oxygen therapy or convalescent plasma, based on therapeutic effectiveness observed for other respiratory illnesses.

### Results

Across SSA, deceased cases for which demographic data are available have been predominantly male (63/103, 61.2%) and over 50 years of age (59/75, 78.7%). In Burkina Faso, specifically, the majority of deceased cases either did not seek care at all or were hospitalized for a single day (59.4%, 19/32); hypertension and diabetes were often reported as underlying conditions. After adjustment for sex, age, and underlying conditions in the synthetic case population, the odds of mortality for cases not receiving oxygen therapy was significantly higher than those receiving oxygen, such as due to disruptions to standard care (OR: 2.07; 95% CI: 1.56 – 2.75). Cases receiving convalescent plasma had 50% reduced odds of mortality than those who did not (95% CI: 0.24 – 0.93).

### Conclusions

Investment in sustainable production and maintenance of supplies for oxygen therapy, along with messaging around early and appropriate use for healthcare providers, caregivers, and patients could reduce COVID-19 deaths in SSA. Further investigation into convalescent plasma is warranted, as data on its effectiveness specifically in treating COVID-19 becomes available. The success of supportive or curative clinical interventions will depend on earlier treatment seeking, such that community engagement and risk communication will be critical components of the response.

Christopher Lorton , Joshua Proctor , Christopher W. Lorton, Joshua L. Proctor, Min K. Roh, Philip A. Welkhoff

CMSB

The compartmental modeling software (CMS) is an open source computational framework that can simulate discrete, stochastic reaction models which are often utilized to describe complex systems from epidemiology and systems biology. In this article, we report the computational requirements, the novel input model language, the available numerical solvers, and the output file format for CMS. In addition, the CMS code repository also includes a library of example model files, unit and regression tests, and documentation. Two examples, one from systems biology and the other from computational epidemiology, are included that highlight the functionality of CMS. We believe the creation of computational frameworks such as CMS will advance our scientific understanding of complex systems as well as encourage collaborative efforts for code development and knowledge sharing.

Joshua Proctor , Isobel Routledge, Shengjie Lai, Katherine E Battle, Azra C Ghani, Manuel Gomez Rodriguez, Kyle B Gustafson, Swapnil Mishra, Joshua L Proctor, Andrew J Tatem, Zhongjie Li, Samir Bhatt

biorxiv

China reported zero locally-acquired malaria cases in 2017 and 2018. Understanding the spatio-temporal pattern underlying this decline, especially the relationship between locally-acquired and imported cases, can inform efforts to maintain elimination and prevent re-emergence. This is particularly pertinent in Yunnan province, where the potential for local transmission is highest. Using a geo-located individual-level dataset of cases recorded in Yunnan province between 2011 and 2016, we jointly estimate the case reproduction number, Rc, and the number of unobserved sources of infection. We use these estimates within spatio-temporal geostatistical models to map how transmission varied over time and space, estimate the timeline to elimination and the risk of resurgence. Our estimates suggest that, maintaining current intervention efforts, Yunnan is unlikely to experience sustained local transmission up to 2020. However, even with a mean Rc of 0.005 projected for the year 2019, locally-acquired cases are possible due to high levels of importation.

Christopher Lorton , Joshua Proctor , Christopher W. Lorton, Joshua L. Proctor, Min K. Roh, Philip A. Welkhoff

BioRxiv

The compartmental modeling software (CMS) is an open source computational framework that can simulate discrete, stochastic reaction models which are often utilized to describe complex systems from epidemiology and systems biology. In this article, we report the computational requirements, the novel input model language, the available numerical solvers, and the output file format for CMS. In addition, the CMS code repository also includes a library of example model files, unit and regression tests, and documentation. Two examples, one from systems biology and the other from computational epidemiology, are included that highlight the functionality of CMS. We believe the creation of computational frameworks such as CMS will advance our scientific understanding of complex systems as well as encourage collaborative efforts for code development and knowledge sharing.

Joshua Proctor , Zhe Bai, Eurika Kaiser, Joshua L. Proctor, J. Nathan Kutz, and Steven L. Brunton

AIAA Journal

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, two recent innovations that extend dynamic mode decomposition to systems with actuation and systems with heavily subsampled measurements are integrated and unified. When combined, these methods yield a novel framework for compressive system identification. It is possible to identify a low-order model from limited input–output data and reconstruct the associated full-state dynamic modes with compressed sensing, adding interpretability to the state of the reduced-order model. Moreover, when full-state data are available, it is possible to dramatically accelerate downstream computations by first compressing the data. This unified framework is demonstrated on two model systems, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). In the first example, this architecture is explored on a test system with known low-rank dynamics and an artificially inflated state dimension. The second example consists of a real-world engineering application given by the fluid flow past a pitching airfoil at low Reynolds number. This example provides a challenging and realistic test case for the proposed method, and results demonstrate that the dominant coherent structures are well characterized despite actuation and heavily subsampled data.

Joshua Proctor , N. M. Mangan , T. Askham , S. L. Brunton , J. N. Kutz and Joshua L. Proctor

Proceedings of the Royal Society A

Hybrid systems are traditionally difficult to identify and analyse using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations solely from measurement data. In this article, we develop a new methodology, Hybrid-Sparse Identification of Nonlinear Dynamics, which identifies separate nonlinear dynamical regimes, employs information theory to manage uncertainty and characterizes switching behaviour. Specifically, we use the nonlinear geometry of data collected from a complex system to construct a set of coordinates based on measurement data and augmented variables. Clustering the data in these measurement-based coordinates enables the identification of nonlinear hybrid systems. This methodology broadly empowers nonlinear system identification without constraining the data locally in time and has direct connections to hybrid systems theory. We demonstrate the success of this method on numerical examples including a mass–spring hopping model and an infectious disease model. Characterizing complex systems that switch between dynamic behaviours is integral to overcoming modern challenges such as eradication of infectious diseases, the design of efficient legged robots and the protection of cyber infrastructures.

Joshua Proctor , Laina D. Mercer, Fred Lu, Joshua L. Proctor

arXiv

Ambitious global goals have been established to provide universal access to affordable modern contraceptive methods. The UN's sustainable development goal 3.7.1 proposes satisfying the demand for family planning (FP) services by increasing the proportion of women of reproductive age using modern methods. To measure progress toward such goals in populous countries like Nigeria, it's essential to characterize the current levels and trends of FP indicators such as unmet need and modern contraceptive prevalence rates (mCPR). Moreover, the substantial heterogeneity across Nigeria and scale of programmatic implementation requires a sub-national resolution of these FP indicators. However, significant challenges face estimating FP indicators sub-nationally in Nigeria. In this article, we develop a robust, data-driven model to utilize all available surveys to estimate the levels and trends of FP indicators in Nigerian states for all women and by age-parity demographic subgroups. We estimate that overall rates and trends of mCPR and unmet need have remained low in Nigeria: the average annual rate of change for mCPR by state is 0.5% (0.4%,0.6%) from 2012-2017. Unmet need by age-parity demographic groups varied significantly across Nigeria; parous women express much higher rates of unmet need than nulliparous women. Our hierarchical Bayesian model incorporates data from a diverse set of survey instruments, accounts for survey uncertainty, leverages spatio-temporal smoothing, and produces probabilistic estimates with uncertainty intervals. Our flexible modeling framework directly informs programmatic decision-making by identifying age-parity-state subgroups with large rates of unmet need, highlights conflicting trends across survey instruments, and holistically interprets direct survey estimates.

Joshua Proctor , Niall M Mangan, Travis Askham, Steven L Brunton, J Nathan Kutz, Joshua L. Proctor

arXiv

Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations solely from measurement data. In this article, we develop a new methodology, Hybrid-Sparse Identification of Nonlinear Dynamics (Hybrid-SINDy), which identifies separate nonlinear dynamical regimes, employs information theory to manage uncertainty, and characterizes switching behavior. Specifically, we utilize the nonlinear geometry of data collected from a complex system to construct a set of coordinates based on measurement data and augmented variables. Clustering the data in these measurement-based coordinates enables the identification of nonlinear hybrid systems. This methodology broadly empowers nonlinear system identification without constraining the data locally in time and has direct connections to hybrid systems theory. We demonstrate the success of this method on numerical examples including a mass-spring hopping model and an infectious disease model. Characterizing complex systems that switch between dynamic behaviors is integral to overcoming modern challenges such as eradication of infectious diseases, the design of efficient legged robots, and the protection of cyber infrastructures.

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Joshua Proctor , Joshua L. Proctor, Steven L. Brunton, J. Nathan Kutz

SIAM journal of Applied Dynamical systems

We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately connected to Dynamic Mode Decomposition (DMD), a method that discovers spatial-temporal coherent modes from data, connects local-linear analysis to nonlinear operator theory, and importantly creates an equation-free architecture allowing investigation of complex systems. In actuated systems, standard Koopman analysis and DMD are incapable of producing input-output models; moreover, the dynamics and the modes will be corrupted by external forcing. Our new theoretical developments extend Koopman operator theory to allow for systems with nonlinear input-output characteristics. We show how this generalization is rigorously connected and generalizes a recent development called Dynamic Mode Decomposition with control (DMDc). We demonstrate this new theory on nonlinear dynamical systems, including a standard Susceptible-Infectious-Recovered model with relevance to the analysis of infectious disease data with mass vaccination (actuation).

Joshua Proctor , Zhe Bai, Eurika Kaiser, Joshua L. Proctor, J. Nathan Kutz, Steven L. Brunton

AIAAJ

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, two recent innovations that extend dynamic mode decomposition to systems with actuation and systems with heavily subsampled measurements are integrated and unified. When combined, these methods yield a novel framework for compressive system identification. It is possible to identify a low-order model from limited input–output data and reconstruct the associated full-state dynamic modes with compressed sensing, adding interpretability to the state of the reduced-order model. Moreover, when full-state data are available, it is possible to dramatically accelerate downstream computations by first compressing the data. This unified framework is demonstrated on two model systems, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). In the first example, this architecture is explored on a test system with known low-rank dynamics and an artificially inflated state dimension. The second example consists of a real-world engineering application given by the fluid flow past a pitching airfoil at low Reynolds number. This example provides a challenging and realistic test case for the proposed method, and results demonstrate that the dominant coherent structures are well characterized despite actuation and heavily subsampled data.

Joshua Proctor , Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, Eurika Kaiser & J. Nathan Kutz

Nature Communications

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth’s magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.

Joshua Proctor , Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor and J. Nathan Kutz

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

Joshua Proctor , Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

Joshua Proctor , Steven L. Brunton, J. Nathan Kutz, and Joshua L. Proctor

SIAM News

Ordinary and partial differential equations are widely used throughout the engineering, physical, and biological sciences to describe the physical laws underlying a given system of interest. We implicitly assume that the governing equations are known and justified by first principles, such as conservation of mass or momentum and/or empirical observations. From the Schrödinger equation of quantum mechanics to Maxwell’s equations for electromagnetic propagation, knowledge of the governing laws has allowed transformative technology (e.g., smart phones, internet, lasers, and satellites) to impact society. In modern applications such as neuroscience, epidemiology, and climate science, the governing equations are only partially known and exhibit strongly nonlinear multiscale dynamics that are difficult to model. Scientific computing methods provide an enabling framework for characterizing such systems, and the SIAM community has historically made some of the most important contributions to simulation-based sciences, including extensive developments in finite-difference, finite-element, spectral, and reduced-order modeling methods.

Joshua Proctor , James M. Kunert, Joshua L. Proctor, Steven L. Brunton, J. Nathan Kutz

PLOS

Using a computational model of the Caenorhabditis elegans connectome dynamics, we show that proprioceptive feedback is necessary for sustained dynamic responses to external input. This is consistent with the lack of biophysical evidence for a central pattern generator, and recent experimental evidence that proprioception drives locomotion. The low-dimensional functional response of the Caenorhabditis elegans network of neurons to proprioception-like feedback is optimized by input of specific spatial wavelengths which correspond to the spatial scale of real body shape dynamics. Furthermore, we find that the motor subcircuit of the network is responsible for regulating this response, in agreement with experimental expectations. To explore how the connectomic dynamics produces the observed two-mode, oscillatory limit cycle behavior from a static fixed point, we probe the fixed point’s low-dimensional structure using Dynamic Mode Decomposition. This reveals that the nonlinear network dynamics encode six clusters of dynamic modes, with timescales spanning three orders of magnitude. Two of these six dynamic mode clusters correspond to previously-discovered behavioral modes related to locomotion. These dynamic modes and their timescales are encoded by the network’s degree distribution and specific connectivity. This suggests that behavioral dynamics are partially encoded within the connectome itself, the connectivity of which facilitates proprioceptive control.

Joshua Proctor , Niall M. Mangan, J. Nathan Kutz, Steven L. Brunton, Joshua L. Proctor

arXiv.org

We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification of nonlinear dynamics algorithm, the sub-selection of candidate models near the Pareto frontier allows for a tractable computation of AIC (Akaike information criteria) or BIC(Bayes information criteria) scores for the remaining candidate models. The information criteria hierarchically ranks the most informative models, enabling the automatic and principled selection of the model with the strongest support in relation to the time series data. Specifically, we show that AIC scores place each candidate model in the strong support, weak support or no support category. The method correctly identifies several canonical dynamical systems, including an SEIR (susceptibleexposed-infectious-recovered) disease model and the Lorenz equations, giving the correct dynamical system as the only candidate model with strong support

Joshua Proctor , Steven L. Brunton, Joshua L. Proctor, J. Nathan Kutz

IFAC-PapersOnLine

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using regression methods, including sparse regression. Specifically, we generalize the sparse identification of nonlinear dynamics (SINDY) algorithm to include external inputs and feedback control. This method is demonstrated on examples including the Lotka-Volterra predator-prey model and the Lorenz system with forcing and control. We also connect the present algorithm with the dynamic mode decomposition (DMD) and Koopman operator theory to provide a broader context.

Joshua Proctor , Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz

AIMS

This work develops compressed sensing strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or compressed data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It is then possible to reconstruct full-state DMD eigenvectors using  1-minimization or greedy algorithms. If full-state snapshots are available, it may be computationally beneficial to compress the data, compute DMD on the compressed data, and then reconstruct full-state modes by applying the compressed DMD transforms to full-state snapshots.

These results rely on a number of theoretical advances. First, we establish connections between DMD on full-state and compressed data. Next, we demonstrate the invariance of the DMD algorithm to left and right unitary transformations. When data and modes are sparse in some transform basis, we show a similar invariance of DMD to measurement matrices that satisfy the restricted isometry property from compressed sensing. We demonstrate the success of this architecture on two model systems. In the first example, we construct a spatial signal from a sparse vector of Fourier coefficients with a linear dynamical system driving the coefficients. In the second example, we consider the double gyre flow field, which is a model for chaotic mixing in the ocean.

Fig. 3

Flow-chart illustrating compressed DMD and compressed sensing DMD.

Joshua Proctor , Joshua L. Proctor, Steven L. Brunton, and J. Nathan Kutz

EPJ

The increasing ubiquity of complex systems that require control is a challenge for existing methodologies in characterization and controller design when the system is high-dimensional, nonlinear, and without physics-based governing equations. We review standard model reduction techniques such as Proper Orthogonal Decomposition (POD) with Galerkin projection and Balanced POD (BPOD). Further, we discuss the link between these equation-based methods and recently developed equation-free methods such as the Dynamic Mode Decomposition and Koopman operator theory. These data-driven methods can mitigate the challenge of not having a well-characterized set of governing equations. We illustrate that this equation-free approach that is being applied to measurement data from complex systems can be extended to include inputs and control. Three specific research examples are presented that extend current equation-free architectures toward the characterization and control of complex systems. These examples motivate a potentially revolutionary shift in the characterization of complex systems and subsequent design of objective-based controllers for data-driven models.

Joshua Proctor , B. W. Brunton, S. L. Brunton, Joshua L. Proctor, and J. N. Kutz

SIAM Journal of Applied Mathematics

Choosing a limited set of sensor locations to characterize or classify a high-dimensional system is an important challenge in engineering design. Traditionally, optimizing the sensor locations involves a brute-force, combinatorial search, which is NP-hard and is computationally intractable for even moderately large problems. Using recent advances in sparsity-promoting techniques, we present a novel algorithm to solve this sparse sensor placement optimization for classification (SSPOC) that exploits low-dimensional structure exhibited by many high-dimensional systems. Our approach is inspired by compressed sensing, a framework that reconstructs data from few measurements. If only classification is required, reconstruction can be circumvented and the measurements needed are orders-of-magnitude fewer still. Our algorithm solves an $\ell_1$ minimization to find the fewest nonzero entries of the full measurement vector that exactly reconstruct the discriminant vector in feature space; these entries represent sensor locations that best inform the decision task. We demonstrate the SSPOC algorithm on five classification tasks, using datasets from a diverse set of examples, including physical dynamical systems, image recognition, and microarray cancer identification. Once training identifies sensor locations, data taken at these locations forms a low-dimensional measurement space, and we perform computationally efficient classification with accuracy approaching that of classification using full-state data. The algorithm also works when trained on heavily subsampled data, eliminating the need for unrealistic full-state training data.

Joshua Proctor , J. Nathan Kutz, Joshua L. Proctor, and Steven L. Brunton

arXiv

We consider the application of Koopman theory to nonlinear partial differential equations. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear dynamics. If such observables can be found, then the dynamic mode decomposition algorithm can be enacted to compute a finite-dimensional approximation of the Koopman operator, including its eigenfunctions, eigenvalues and Koopman modes. Judiciously chosen observables lead to physically interpretable spatio-temporal features of the complex system under consideration and provide a connection to manifold learning methods. We demonstrate the impact of observable selection, including kernel methods, and construction of the Koopman operator on two canonical, nonlinear PDEs: Burgers’ equation and the nonlinear Schr¨odinger equation. These examples serve to highlight the most pressing and critical challenge of Koopman theory: a principled way to select appropriate observables.

Joshua Proctor , Niall M. Mangan, Steven L. Brunton, Joshua L. Proctor, J. Nathan Kutz

IEEE Transactions on Molecular, Biological, and Multi-Scale Communications

Inferring the structure and dynamics of network models is critical to understanding the functionality and control of complex systems, such as metabolic and regulatory biological networks. The increasing quality and quantity of experimental data enable statistical approaches based on information theory for model selection and goodness-of-fit metrics. We propose an alternative data-driven method to infer networked nonlinear dynamical systems by using sparsity-promoting optimization to select a subset of nonlinear interactions representing dynamics on a network. In contrast to standard model selection methods-based upon information content for a finite number of heuristic models (order 10 or less), our model selection procedure discovers a parsimonious model from a combinatorially large set of models, without an exhaustive search. Our particular innovation is appropriate for many biological networks, where the governing dynamical systems have rational function nonlinearities with cross terms, thus requiring an implicit formulation and the equations to be identified in the null-space of a library of mixed nonlinearities, including the state and derivative terms. This method, implicit-SINDy, succeeds in inferring three canonical biological models: 1) Michaelis-Menten enzyme kinetics; 2) the regulatory network for competence in bacteria; and 3) the metabolic network for yeast glycolysis.

Joshua Proctor , Steven L. Brunton, Joshua L. Proctor and J. Nathan Kutz

PNAS

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

Joshua Proctor , Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, J. Nathan Kutz

PLoS ONE

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state.

Joshua Proctor , Joshua L. Proctor, S. L. Brunton, B. W. Brunton, J. N. Kutz

SIAM Journal on Applied Dynamical Systems

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear analysis to nonlinear operator theory, and provides an equation-free architecture which is compatible with compressive sensing. In actuated systems, DMD is incapable of producing an input-output model; moreover, the dynamics and the modes will be corrupted by external forcing. Our new method, Dynamic Mode Decomposition with control (DMDc), capitalizes on all of the advantages of DMD and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models. The method is data-driven in that it does not require knowledge of the underlying governing equations, only snapshots of state and actuation data from historical, experimental, or black-box simulations. We demonstrate the method on high dimensional dynamical systems, including a model with relevance to the analysis of infectious disease data with mass vaccination (actuation).

Joshua Proctor , Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor, J. Nathan Kutz

arXiv.org, Cornell University Library

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to a subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves observable functions on the state-space of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear observations of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. It remains an open challenge how to choose the right nonlinear observable functions to form a subspace where it is possible to obtain efficient linear reduced-order models.

Here, we investigate the choice of observable functions for Koopman analysis. First, we note that in order to obtain a linear Koopman system that advances the original states, it is helpful to include these states in the observable subspace, as in DMD. We then categorize dynamical systems by whether or not there exists a Koopman-invariant observable subspace that includes the state variables as observables. In particular, we note that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not topologically conjugate to a finite-dimensional linear system; this is illustrated using the logistic map. Second, we present a data-driven strategy to identify the relevant observable functions for Koopman analysis. We leverage a new algorithm that determines relevant terms in a dynamical system by 1 regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Joshua Proctor , Steven L. Brunton, Joshua L. Proctor, J. Nathan Kutz

arXiv.org, Cornell University Library

The ability to discover physical laws and governing equations from data is one of humankind’s greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled advanced technological achievements, including aircraft, combustion engines, satellites, and electrical power. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing physical equations from measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized, time-varying, or externally forced systems.

Joshua Proctor , Joshua L. Proctor, Philip A. Eckhoff

International Health

Background

The development and application of quantitative methods to understand disease dynamics and plan interventions is becoming increasingly important in the push toward eradication of human infectious diseases, exemplified by the ongoing effort to stop the spread of poliomyelitis.

Methods

Dynamic mode decomposition (DMD) is a recently developed method focused on discovering coherent spatial-temporal modes in high-dimensional data collected from complex systems with time dynamics. The algorithm has a number of advantages including a rigorous connection to the analysis of nonlinear systems, an equation-free architecture, and the ability to efficiently handle high-dimensional data.

Results

We demonstrate the method on three different infectious disease sets including Google Flu Trends data, pre-vaccination measles in the UK, and paralytic poliomyelitis wild type-1 cases in Nigeria. For each case, we describe the utility of the method for surveillance and resource allocation.

Conclusions

We demonstrate how DMD can aid in the analysis of spatial-temporal disease data. DMD is poised to be an effective and efficient computational analysis tool for the study of infectious disease.

Joshua Proctor , Matthew O. Williams, Joshua Proctor, J. Nathan Kutz

Physica D

Although disease transmission in the near eradication regime is inherently stochastic, deterministic quantities such as the probability of eradication are of interest to policy makers and researchers. Rather than running large ensembles of discrete stochastic simulations over long intervals in time to compute these deterministic quantities, we create a data-driven and deterministic “coarse” model for them using the Equation Free (EF) framework. In lieu of deriving an explicit coarse model, the EF framework approximates any needed information, such as coarse time derivatives, by running short computational experiments. However, the choice of the coarse variables (i.e., the state of the coarse system) is critical if the resulting model is to be accurate. In this manuscript, we propose a set of coarse variables that result in an accurate model in the endemic and near eradication regimes, and demonstrate this on a compartmental model representing the spread of Poliomyelitis. When combined with adaptive time-stepping coarse projective integrators, this approach can yield over a factor of two speedup compared to direct simulation, and due to its lower dimensionality, could be beneficial when conducting systems level tasks such as designing eradication or monitoring campaigs.

Joshua Proctor , Joshua L. Proctor, S. L. Brunton, B. W. Brunton, J. N. Kutz

arXiv.org, Cornell University Library

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear analysis to nonlinear operator theory, and provides an equation-free architecture which is compatible with compressive sensing. In actuated systems, DMD is incapable of producing an input-output model; moreover, the dynamics and the modes will be corrupted by external forcing. Our new method, Dynamic Mode Decomposition with control (DMDc), capitalizes on all of the advantages of DMD and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models. The method is data-driven in that it does not require knowledge of the underlying governing equations, only snapshots of state and actuation data from historical, experimental, or black-box simulations. We demonstrate the method on high dimensional dynamical systems, including a model with relevance to the analysis of infectious disease data with mass vaccination (actuation).

Joshua Proctor , Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz

arXiv.org, Cornell University Library

This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It is then possible to reconstruct full-state DMD eigenvectors using ℓ1-minimization or greedy algorithms. If full-state snapshots are available, it may be computationally beneficial to compress the data, compute a compressed DMD, and then reconstruct full-state modes by applying the projected DMD transforms to full-state snapshots.
These results rely on a number of theoretical advances. First, we establish connections between the full-state and projected DMD. Next, we demonstrate the invariance of the DMD algorithm to left and right unitary transformations. When data and modes are sparse in some transform basis, we show a similar invariance of DMD to measurement matrices that satisfy the so-called restricted isometry principle from compressive sampling. We demonstrate the success of this architecture on two model systems. In the first example, we construct a spatial signal from a sparse vector of Fourier coefficients with a linear dynamical system driving the coefficients. In the second example, we consider the double gyre flow field, which is a model for chaotic mixing in the ocean.

The enterics research program at IDM provides analytic support to research, policy, and implementation partners on a range of diseases, including typhoid fever, cholera, and a variety of pathogens responsible for childhood diarrhea.

Our typhoid research centers on questions of elimination feasibility and impact forecasting under different vaccination and WASH strategies. To support these efforts, we use mathematical modeling to describe mechanistically how different transmission routes -- human-to-human contact vs. environmental -- relate to setting-specific patterns of disease incidence, specifically spatial clustering, age patterns, environmental surveillance, and genetic signatures. For more information on typhoid research, please contact Jillian Gauld.

Our cholera research has focused on building spatial dynamical models of disease transmission and evaluating vaccine efficacy profiles to inform policy in endemic settings and outbreak scenarios. For more information on cholera research, please contact Dennis Chao.

More broadly, our research on diarrhea, a leading cause of childhood mortality, has explored the age and seasonal dependence of different viral, bacterial, and protozoal pathogens across numerous geographic settings. The goal has been to elucidate complex epidemiological pathogens, inform improved clinical decision-making, and contextualize the information-value of different diagnostic characteristics.

Some areas of work include:

• Typhoid risk factors in Malawi
• Seasonality of Diarrheal Pathogens
• Efficacy of Cholera Vaccine
• MDR non-typhoid salmonella in Kenya

Dennis Chao , Joshua Proctor , Ben J Brintz, Benjamin Haaland, Joel Howard, Dennis L Chao, Joshua L Proctor, Ashraful I Khan, Sharia M Ahmed, Lindsay T Keegan, Tom Greene

eLife

Traditional clinical prediction models focus on parameters of the individual patient. For infectious diseases, sources external to the patient, including characteristics of prior patients and seasonal factors, may improve predictive performance. We describe the development of a predictive model that integrates multiple sources of data in a principled statistical framework using a post-test odds formulation. Our method enables electronic real-time updating and flexibility, such that components can be included or excluded according to data availability. We apply this method to the prediction of etiology of pediatric diarrhea, where 'pre-test’ epidemiologic data may be highly informative. Diarrhea has a high burden in low-resource settings, and antibiotics are often over-prescribed. We demonstrate that our integrative method outperforms traditional prediction in accurately identifying cases with a viral etiology, and show that its clinical application, especially when used with an additional diagnostic test, could result in a 61% reduction in inappropriately prescribed antibiotics.

Dennis Chao , Joshua Proctor , Dennis L. Chao, Anna Roose, Min Roh, Karen L. Kotloff, Joshua L. Proctor

PLos NTDs

### Background

Pediatric diarrhea can be caused by a wide variety of pathogens, from bacteria to viruses to protozoa. Pathogen prevalence is often described as seasonal, peaking annually and associated with specific weather conditions. Although many studies have described the seasonality of diarrheal disease, these studies have occurred predominantly in temperate regions. In tropical and resource-constrained settings, where nearly all diarrhea-associated mortality occurs, the seasonality of many diarrheal pathogens has not been well characterized. As a retrospective study, we analyze the seasonal prevalence of diarrheal pathogens among children with moderate-to-severe diarrhea (MSD) over three years from the seven sites of the Global Enteric Multicenter Study (GEMS), a case–control study. Using data from this expansive study on diarrheal disease, we characterize the seasonality of different pathogens, their association with site-specific weather patterns, and consistency across study sites.

### Methodology/Principal findings

Using traditional methodologies from signal processing, we found that certain pathogens peaked at the same time every year, but not at all sites. We also found associations between pathogen prevalence and weather or “seasons,” which are defined by applying modern machine-learning methodologies to site-specific weather data. In general, rotavirus was most prevalent during the drier “winter” months and out of phase with bacterial pathogens, which peaked during hotter and rainier times of year corresponding to “monsoon,” “rainy,” or “summer” seasons.

### Conclusions/Significance

Identifying the seasonally-dependent prevalence for diarrheal pathogens helps characterize the local epidemiology and inform the clinical diagnosis of symptomatic children. Our multi-site, multi-continent study indicates a complex epidemiology of pathogens that does not reveal an easy generalization that is consistent across all sites. Instead, our study indicates the necessity of local data to characterizing the epidemiology of diarrheal disease. Recognition of the local associations between weather conditions and pathogen prevalence suggests transmission pathways and could inform control strategies in these settings.

Joshua Proctor , Dennis Chao , Dennis L Chao, Anna Roose, Min Roh, Karen L Kotloff, Joshua L. Proctor

bioarxiv

Background: Pediatric diarrhea can be caused by a wide variety of pathogens, from bacteria to viruses to protozoa. Pathogen prevalence is often described as seasonal, peaking annually and associated with specific weather conditions. Although many studies have described the seasonality of diarrheal disease, these studies have occurred predominantly in temperate regions. In tropical and resource-constrained settings, where nearly all diarrhea-associated mortality occurs, the seasonality of many diarrheal pathogens has not been well characterized. As a retrospective study, we analyze the seasonal prevalence of diarrheal pathogens among children with moderate-to-severe diarrhea (MSD) over three years from the seven sites of the Global Enteric Multicenter Study (GEMS). Using data from this expansive study on diarrheal disease, we characterize the seasonality of different pathogens, their association with site-specific weather patterns, and consistency across study sites. Methodology/Principal Findings: Using traditional methodologies from signal processing, we found that certain pathogens peaked at the same time every year, but not at all sites. We also found associations between pathogen prevalence and weather or "seasons", which are defined by applying modern machine-learning methodologies to site-specific weather data. In general, rotavirus was most prevalent during the drier "winter" months and out of phase with bacterial pathogens, which peaked during hotter and rainier times of year corresponding to "monsoon", "rainy", or "summer" seasons. Conclusions/Significance: Identifying the seasonally-dependent prevalence for diarrheal pathogens helps characterize the local epidemiology and inform the clinical diagnosis of symptomatic children. Our multi-site, multi-continent study indicates a complex epidemiology of pathogens that does not reveal an easy generalization that is consistent across all sites. Instead, our study indicates the necessity of local data to characterizing the epidemiology of diarrheal disease. Recognition of the local associations between weather conditions and pathogen prevalence suggests transmission pathways and could inform control strategies in these settings.

Dennis Chao , Youyi Fong, M. Elizabeth Halloran, Jin Kyung Park, Florian Marks, John D. Clemens and Dennis L. Chao

BMC Infectious Diseases

### Background

Oral cholera vaccine (OCV) is a feasible tool to prevent or mitigate cholera outbreaks. A better understanding of the vaccine’s efficacy among different age groups and how rapidly its protection wanes could help guide vaccination policy.

### Methods

To estimate the level and duration of OCV efficacy, we re-analyzed data from a previously published cluster-randomized, double-blind, placebo controlled trial with five years of follow-up. We used a Cox proportional hazards model and modeled the potentially time-dependent effect of age categories on both vaccine efficacy and risk of infection in the placebo group. In addition, we investigated the impact of an outbreak period on model estimation.

### Results

Vaccine efficacy was 38% (95% CI: -2%,62%) for those vaccinated from ages 1 to under 5 years old, 85% (95% CI: 67%,93%) for those 5 to under 15 years, and 69% (95% CI: 49%,81%) for those vaccinated at ages 15 years and older. Among adult vaccinees, efficacy did not appear to wane during the trial, but there was insufficient data to assess the waning of efficacy among child vaccinees.

### Conclusions

Through this re-analysis we were able to detect a statistically significant difference in OCV efficacy when the vaccine was administered to children under 5 years old vs. children 5 years and older. The estimated efficacies are more similar to the previously published analysis based on the first two years of follow-up than the analysis based on all five years.

Dennis Chao , Thomas J. Hladish, Carl A. B. Pearson, Dennis Chao, Diana Patricia Rojas, Gabriel L. Recchia, Héctor Gómez-Dantés, M. Elizabeth Halloran, Juliet R. C. Pulliam, Ira M. Longini

PLOS Neglected Tropical Diseases

Dengue vaccines will soon provide a new tool for reducing dengue disease, but the effectiveness of widespread vaccination campaigns has not yet been determined. We developed an agent-based dengue model representing movement of and transmission dynamics among people and mosquitoes in Yucatán, Mexico, and simulated various vaccine scenarios to evaluate effectiveness under those conditions. This model includes detailed spatial representation of the Yucatán population, including the location and movement of 1.8 million people between 375,000 households and 100,000 workplaces and schools. Where possible, we designed the model to use data sources with international coverage, to simplify re-parameterization for other regions. The simulation and analysis integrate 35 years of mild and severe case data (including dengue serotype when available), results of a seroprevalence survey, satellite imagery, and climatological, census, and economic data. To fit model parameters that are not directly informed by available data, such as disease reporting rates and dengue transmission parameters, we developed a parameter estimation toolkit called AbcSmc, which we have made publicly available. After fitting the simulation model to dengue case data, we forecasted transmission and assessed the relative effectiveness of several vaccination strategies over a 20 year period. Vaccine efficacy is based on phase III trial results for the Sanofi-Pasteur vaccine, Dengvaxia. We consider routine vaccination of 2, 9, or 16 year-olds, with and without a one-time catch-up campaign to age 30. Because the durability of Dengvaxia is not yet established, we consider hypothetical vaccines that confer either durable or waning immunity, and we evaluate the use of booster doses to counter waning. We find that plausible vaccination scenarios with a durable vaccine reduce annual dengue incidence by as much as 80% within five years. However, if vaccine efficacy wanes after administration, we find that there can be years with larger epidemics than would occur without any vaccination, and that vaccine booster doses are necessary to prevent this outcome.

For rapidly evolving pathogens, evolution complicates infectious disease control. Pathogen evolution can be thought of as taking place in a complex landscape influenced by the interactions between pathogen and host genetics, ecology, and epidemiology. This mandates an interdisciplinary approach that combines ideas from these fields into unified models.

At IDM, we focus on using dynamic, evolutionary disease transmission models to study evolutionary epidemiology phenomena. Specifically, we seek to model the emergence and spread of infectious diseases in realistic settings where natural selection, genetic drift, and genetic recombination/reassortment play key roles in the epidemic process.

We believe this approach will result in better disease management and public health policies in situations where interventions influence and are influenced by pathogen evolution. Although related to genomic epi, our work on evolutionary epi focuses on the dynamics of phenotypic evolution and is not solely focused on modeling sequencing data. Currently, our primary focus is modeling the emergence of cVDPV following mOPV2 administration. Future areas of interest include zoonotic emergence, drug resistance management, and CRISPR/CAS mutations.

The family planning team at the Institute for Disease Modeling is dedicated to informing decision-making to help achieve global goals to increase access to affordable, effective, and safe family planning services. Ensuring universal access and meeting demand for family planning services is integral to achieving gender equality, increasing economic empowerment, and improving health outcomes. We utilize data-driven approaches, such as dynamic modeling, statistical analyses, and machine-learning, to help characterize the current challenges facing the family planning community. Moreover, our analytic approaches leverage existing data to support policy and funding decisions in resource-constrained settings. We collaborate with governmental and non-governmental agencies as well as in-country partners to ensure analyses are directly relevant to informing family planning interventions and optimizing their implementation.

Joshua Proctor , Laina D. Mercer, Fred Lu &  Joshua L. Proctor

BMC Public Health

### Background

Ambitious global goals have been established to provide universal access to affordable modern contraceptive methods. To measure progress toward such goals in populous countries like Nigeria, it’s essential to characterize the current levels and trends of family planning (FP) indicators such as unmet need and modern contraceptive prevalence rates (mCPR). Moreover, the substantial heterogeneity across Nigeria and scale of programmatic implementation requires a sub-national resolution of these FP indicators. The aim of this study is to estimate the levels and trends of FP indicators at a subnational scale in Nigeria utilizing all available data and accounting for survey design and uncertainty.

### Methods

We utilized all available cross-sectional survey data from Nigeria including the Demographic and Health Surveys, Multiple Indicator Cluster Surveys, National Nutrition and Health Surveys, and Performance, Monitoring, and Accountability 2020. We developed a hierarchical Bayesian model that incorporates all of the individual level data from each survey instrument, accounts for survey uncertainty, leverages spatio-temporal smoothing, and produces probabilistic estimates with uncertainty intervals.

### Results

We estimate that overall rates and trends of mCPR and unmet need have remained low in Nigeria: the average annual rate of change for mCPR by state is 0.5% (0.4%,0.6%) from 2012-2017. Unmet need by age-parity demographic groups varied significantly across Nigeria; parous women express much higher rates of unmet need than nulliparous women.

### Conclusions

Understanding the estimates and trends of FP indicators at a subnational resolution in Nigeria is integral to inform programmatic decision-making. We identify age-parity-state subgroups with large rates of unmet need. We also find conflicting trends by survey instrument across a number of states. Our model-based estimates highlight these inconsistencies, attempt to reconcile the direct survey estimates, and provide uncertainty intervals to enable interpretation of model and survey estimates for decision-making.

The genomic epidemiology research program at IDM analyzes pathogen genomic data, in the context of other routine surveillance data, to resolve characteristics of disease transmission and enable improved programmatic decision-making. To support these efforts, we are researching improved methods for genetic-feature engineering, approximate

Bayesian inference, and forward-simulation platforms. Focus areas for applications of this work include malaria, polio, flu, typhoid, HIV, and Ebola.

• Malaria – Josh Proctor and Albert Lee
• Polio – Steve Kroiss, Wesley Wong, Mike Famulare
• Flu – Greg Hart, Rafael Nunez, Mike Famulare

Some areas of work include:

• Identifying Spatiotemporal Dynamics of Ebola in Sierra Leone Using Virus Genomes
• Modeling Malaria Genomics Reveals Transmission Decline and Rebound in Senegal

Bradley Wagner , Bradley H. Wagenaar, Orvalho Augusto, Kristjana Ásbjörnsdóttir, Adam Akullian, Nelia Manaca, Falume Chale, Alberto Muanido, Alfredo Covele, Cathy Michel, Sarah Gimbel, Tyler Radford, Blake Girardot, Kenneth Sherr

International Journal of Health Geographics

### Background

Lack of accurate data on the distribution of sub-national populations in low- and middle-income countries impairs planning, monitoring, and evaluation of interventions. Novel, low-cost methods to develop unbiased survey sampling frames at sub-national, sub-provincial, and even sub-district levels are urgently needed. This article details our experience using remote satellite imagery to develop a provincial-level representative community survey sampling frame to evaluate the effects of a 7-year health system intervention in Sofala Province, Mozambique.

### Methods

Mozambique’s most recent census was conducted in 2007, and no data are readily available to generate enumeration areas for representative health survey sampling frames. To remedy this, we partnered with the Humanitarian OpenStreetMap Team to digitize every building in Sofala and Manica provinces (685,189 Sofala; 925,713 Manica) using up-to-date remote satellite imagery, with final results deposited in the open-source OpenStreetMap database. We then created a probability proportional to size sampling frame by overlaying a grid of 2.106 km resolution (0.02 decimal degrees) across each province, and calculating the number of buildings within each grid square. Squares containing buildings were used as our primary sampling unit with replacement. Study teams navigated to the geographic center of each selected square using geographic positioning system coordinates, and then conducted a standard “random walk” procedure to select 20 households for each time a given square was selected. Based on sample size calculations, we targeted a minimum of 1500 households in each province. We selected 88 grids within each province to reach 1760 households, anticipating ongoing conflict and transport issues could preclude the inclusion of some clusters.

### Results

Civil conflict issues forced the exclusion of 8 of 31 subdistricts in Sofala and 15 of 39 subdistricts in Manica. Using Android tablets, Open Data Kit software, and a remote RedCap data capture system, our final sample included 1549 households in Sofala (4669 adults; 4766 children; 33 missing age) and 1538 households in Manica (4422 adults; 4898 children; 33 missing age).

### Conclusions

Other implementation or evaluation teams may consider employing similar methods to track population distributions for health systems planning or the development of representative sampling frames using remote satellite imagery.

Edward Wenger , Sean M. Moore, Quirine A. ten Bosch, Amir S. Siraj, K. James Soda, Guido España, Alfonso Campo, Sara Gómez, Daniela Salas, Benoit Raybaud, Edward Wenger, Philip Welkhoff and T. Alex Perkins

BMC Medicine

Mathematical models of transmission dynamics are routinely fitted to epidemiological time series, which must inevitably be aggregated at some spatial scale. Weekly case reports of chikungunya have been made available nationally for numerous countries in the Western Hemisphere since late 2013, and numerous models have made use of this data set for forecasting and inferential purposes. Motivated by an abundance of literature suggesting that the transmission of this mosquito-borne pathogen is localized at scales much finer than nationally, we fitted models at three different spatial scales to weekly case reports from Colombia to explore limitations of analyses of nationally aggregated time series data.

### Methods

We adapted the recently developed Disease Transmission Kernel (DTK)-Dengue model for modeling chikungunya virus (CHIKV) transmission, given the numerous similarities of these viruses vectored by a common mosquito vector. We fitted versions of this model specified at different spatial scales to weekly case reports aggregated at different spatial scales: (1) single-patch national model fitted to national data; (2) single-patch departmental models fitted to departmental data; and (3) multi-patch departmental models fitted to departmental data, where the multiple patches refer to municipalities within a department. We compared the consistency of simulations from fitted models with empirical data.

### Results

We found that model consistency with epidemic dynamics improved with increasing spatial granularity of the model. Specifically, the sum of single-patch departmental model fits better captured national-level temporal patterns than did a single-patch national model. Likewise, multi-patch departmental model fits better captured department-level temporal patterns than did single-patch departmental model fits. Furthermore, inferences about municipal-level incidence based on multi-patch departmental models fitted to department-level data were positively correlated with municipal-level dat that were withheld from model fitting.

Adam Akullian , Adam Akullian , Joel M. Montgomery, Grace John-Stewart, Samuel I. Miller, Hillary S. Hayden, Matthew C. Radey, Kyle R. Hager, Jennifer R. Verani, John Benjamin Ochieng, Jane Juma, Jim Katieno, Barry Fields, Godfrey Bigogo, Allan Audi, Judd Walson

PLOS Neglected Tropical Diseases

Non-typhoidal Salmonella (NTS) is a leading cause of bloodstream infections in Africa, but the various contributions of host susceptibility versus unique pathogen virulence factors are unclear. We used data from a population-based surveillance platform (population ~25,000) between 2007–2014 and NTS genome-sequencing to compare host and pathogen-specific factors between individuals presenting with NTS bacteremia and those presenting with NTS diarrhea. Salmonella Typhimurium ST313 and Salmonella Enteritidis ST11 were the most common isolates. Multi-drug resistant strains of NTS were more commonly isolated from patients presenting with NTS bacteremia compared to NTS diarrhea. This relationship was observed in patients under age five [aOR = 15.16, 95% CI (2.84–81.05), P = 0.001], in patients five years and older, [aOR = 6.70 95% CI (2.25–19.89), P = 0.001], in HIV-uninfected patients, [aOR = 21.61, 95% CI (2.53–185.0), P = 0.005], and in patients infected with Salmonella serogroup B [aOR = 5.96, 95% CI (2.28–15.56), P < 0.001] and serogroup D [aOR = 14.15, 95% CI (1.10–182.7), P = 0.042]. Thus, multi-drug-resistant NTS was strongly associated with bacteremia compared to diarrhea among children and adults. This association was seen in HIV-uninfected individuals infected with either S. Typhimurium or S. Enteritidis. Risk of developing bacteremia from NTS infection may be driven by virulence properties of the Salmonella pathogen.

The health delivery research program at IDM provides research and analysis in support of global, country-level, and subnational health delivery goals and strategy, with particular emphasis on immunization. This research is concerned with quantitative analysis of health outcomes and delivery goals in relation to existing health delivery systems, interventions, programs, policies, and socioeconomic drivers. We achieve these research aims with a team of diverse expertise, with statistical, health economic, and cost modeling of datasets and synthesis of scientific evidence. We encourage you to reach out to our team to learn more and collaborate.

Current projects in our research portfolio include:

• Health equity analysis; patterns, prospects, efficiency, and evidence for health equity goals
• Socioeconomic drivers of routine immunization
• Health system strengthening interventions
• Drivers of health system access and effectiveness (e.g. behaviors, access to care, workforce, structures)

Our health economics team aims to enhance ongoing disease modeling research by exploring additional factors relevant to makers, such as budget or logistical constraints, trade-offs between intervention strategies, or non-health outcomes. We focus on projects with real-time use by and application for decision maker, and translation into policy decisions. Decision makers are under continuous pressure to demonstrate greater accountability for how limited health resources are used to meet health system goals, which is an interconnected and time-dependent decision process.

There is a substantial body of published research on the cost-effectiveness of individual interventions in the global health and infectious disease areas, but there are practical and methodological challenges that limit the application of this research. At IDM we strive to extend this existing body of research by linking finance and disease modeling methods. We often do so by integrating health economics methods with the results of robust disease transmission models developed by IDM’s disease modeling teams.

Several key methodologies include:

• Cost-effectiveness and cost-utility analyses (CEA/CUA): Using these models, we incorporate the costs of vaccination, treatment, implementation, or other features to compare multiple intervention strategies in terms of value for money. We focus on making these models relevant to the questions asked by decision makers and presented in a user-friendly format or tool.
• Value of Information or data (VoI): These methods are used to qualify the impact of uncertainty in decision making. VoI combines the uncertainty in modeling and data with the impact of decisions to define the need of more accurate data. VoI can also be applied to data needs, such as disease surveillance, quantify the value or investing in data acquisition interventions instead of or in addition to other health interventions.
• Program budgeting and marginal analysis (PMBA): This type of analysis can be used to make recommendations for optimizing a portfolio or program under a budget constraint. It incorporates locally relevant decision-making criteria, multi-criteria decision analysis, investments and disinvestments, and aligns options with each specific analysis.

Brittany Hagedorn , Jillian Gauld , Brittany L. Hagedorn, Jillian Gauld, Nicholas Feasey, Hao Hu

Vaccine

Since the prequalification of the Typhoid conjugate vaccine (TCV) by the WHO and subsequent position paper published in 2018, strategies for roll-out of the vaccine have been under discussion [1]. The 2018 position paper recommends the introduction of TCV to be prioritized in countries with the highest burden of typhoid disease or a high burden of antimicrobial resistant S. Typhi [1]. The paper further suggests that “Decisions on the age of TCV administration, target population and delivery strategy for routine and catch-up vaccination should be based on the local epidemiology of typhoid fever…”. However, local epidemiology of typhoid fever is often poorly documented, due to the paucity of diagnostic facilities in many high typhoid incidence settings. However, most low- and middle income- countries (LMIC) rely on ad hoc reporting of typhoid fever, and very few have data from more than one city in the country. There have been substantial efforts aimed at strengthening blood culture surveillance for typhoid fever in Africa [2], yet there are still only 13 sentinel sites in 10 countries; a similar initiative in Asia covers only four countries [3]. Data sets that are utilized to estimate global burden are therefore limited by the lack of surveillance [4][5][6][7]. Based on the prohibitive costs [2] and efforts required to strengthen blood culture surveillance in LMIC, expansion of these efforts to capture both national and sub-national trends of typhoid on a global scale are not likely on a time scale relevant to vaccine roll-out.

Incidence mapping using statistical models can aid in predicting incidence in areas without surveillance, using spatial covariates relevant to risk of disease, and has been used for diseases such as malaria [8]. This approach has been attempted for typhoid through global burden models [4], but out-of-sample validation, though accurate in some areas, was not reliable, indicating a lack of useful indicators that can be consistently used to predict typhoid incidence. Further, the current breadth of data is heavily biased by reporting from a handful of well-funded sites, so predicting sub-national incidence across large regions is a challenge. A country’s ability to roll out TCV in accordance with the WHO’s position paper is therefore hindered by a lack of knowledge of local epidemiology of the disease. Additionally, Gavi, The Vaccine Alliance, recommends that countries requesting TCV funding should submit epidemiological data from within-country whenever possible, though this is not strictly a requirement.

Alternative tools are needed for planning TCV strategies in the absence of blood culture surveillance. Of particular interest is environmental surveillance, where, instead of relying on clinical detection of the disease, catchments in the environment such as water or sewage systems are surveilled. This approach has been successfully used in the polio eradication campaign. [9] Though case-based surveillance for polio is widespread, the disease is known to undergo sub-clinical (silent) transmission. ES has enabled detection when there is not a known outbreak and has been demonstrated to be a useful tool in program decision making [10][11]. Since typhoid and polio share similarities with regards to transmission routes and sub-clinical disease, it is possible that the approach and the network of laboratories developed for polio could be adapted for typhoid.

There remain significant technical challenges to implementing typhoid environmental surveillance (ES); optimal sampling strategies and detection methods, and their reliability as an indicator of ongoing transmission, remain unclear. Historically, Moore swabs have been used to isolate S. Typhi from sewage [12][13], however present day ES initiatives have been more focused on molecular approaches, specifically polymerase chain reaction (PCR)-based detection of S Typhi [14][15][16].

Economic analyses have largely supported the cost-effectiveness of the roll out of TCV in high and medium- incidence areas, particularly when routine vaccination strategies are paired with catch-up campaigns [17][18], however, there is more uncertainty around cost-effectiveness in low-incidence areas [19]. In this study, we examine the use of a hypothetical environmental surveillance program as a method for quickly gathering evidence on which an introduction decision can be based. This is especially relevant in places where there are inadequate burden estimates or in which a national introduction may not be affordable due to funding constraints or competing priorities. Specifically, we evaluate the value of environmental sampling as a means of detecting circulating typhoid in order to guide local or national targeting of catch-up vaccination campaigns. We aim to determine the most cost-effective sampling and roll-out strategies, given the limited information and substantial uncertainty about the true underlying prevalence of typhoid.

Brittany Hagedorn , Kevin McCarthy , Brittany L. Hagedorn, Alya Dabbagh, Kevin A. McCarthy

Vaccine

Measles vaccination is a cost-effective way to prevent infection and reduce mortality and morbidity. However, in countries with fragile routine immunization infrastructure, coverage rates are still low and supplementary immunization campaigns (SIAs) are used to reach previously unvaccinated children. During campaigns, vaccine is generally administered to every child, regardless of their vaccination status and as a result, there is the possibility that a child that is already immune to measles (i.e. who has had 2+ vaccinations) would receive an unnecessary dose, resulting in excess cost. Selective vaccination has been proposed as one solution to this; children who were able to provide documentation of previous vaccination would not be vaccinated repeatedly. While this would result in reduced vaccine and supply cost, it would also require additional staff time and increased social mobilization investment, potentially outweighing the benefits. We utilize Monte Carlo simulation to assess under what conditions a selective vaccination policy would indeed result in net savings. We demonstrate that cost savings are possible in contexts with a high joint probability of an individual child having both 2+ previous measles doses and also an available record. We also find that the magnitude of net cost savings is highly dependent on whether a country is using measles-only or measles-rubella vaccine and on the required skill set of the individual who would review the previous vaccination records.

Marita Zimmermann , Kurt Frey , Brittany Hagedorn , Kevin McCarthy , Guillaume Chabot-Couture , Marita Zimmermann, Kurt Frey, Brittany Hagedorn, A.J.Oteri, Abdulazeez Yahya, Maimuna Hamisu, Fred Mogekwu, Faisal Shuaib, Kevin A.McCarthy, Guillaume Chabot-Couture

Vaccine

### Background

Measles causes significant childhood morbidity in Nigeria. Routine immunization (RI) coverage is around 40% country-wide, with very high levels of spatial heterogeneity (3–86%), with supplemental immunization activities (SIAs) at 2-year or 3-year intervals. We investigated cost savings and burden reduction that could be achieved by adjusting the inter-campaign interval by region.

### Methods

We modeled 81 scenarios; permuting SIA calendars of every one, two, or three years in each of four regions of Nigeria (North-west, North-central, North-east, and South). We used an agent-based disease transmission model to estimate the number of measles cases and ingredients-based cost models to estimate RI and SIA costs for each scenario over a 10 year period.

### Results

Decreasing SIAs to every three years in the North-central and South (regions of above national-average RI coverage) while increasing to every year in either the North-east or North-west (regions of below national-average RI coverage) would avert measles cases (0.4 or 1.4 million, respectively), and save vaccination costs (save $19.4 or$5.4 million, respectively), compared to a base-case of national SIAs every two years. Decreasing SIA frequency to every three years in the South while increasing to every year in the just the North-west, or in all Northern regions would prevent more cases (2.1 or 5.0 million, respectively), but would increase vaccination costs (add $3.5 million or$34.6 million, respectively), for $1.65 or$6.99 per case averted, respectively.

### Conclusions

Our modeling shows how increasing SIA frequency in Northern regions, where RI is low and birth rates are high, while decreasing frequency in the South of Nigeria would reduce the number of measles cases with relatively little or no increase in vaccination costs. A national vaccination strategy that incorporates regional SIA targeting in contexts with a high level of sub-national variation would lead to improved health outcomes and/or lower costs.

Brittany Hagedorn , Assaf Oron , Wedlock PT, Mitgang EA, Oron AP, Hagedorn BL, Leonard J, Brown ST, Bakal J, Siegmund SS, Lee BY

Vaccine

#### INTRODUCTION:

The lack of specific policies on how many children must be present at a vaccinating location before a healthcare worker can open a measles-containing vaccine (MCV) - i.e. the vial-opening threshold - has led to inconsistent practices, which can have wide-ranging systems effects.

#### METHODS:

Using HERMES-generated simulation models of the routine immunization supply chains of Benin, Mozambique and Niger, we evaluated the impact of different vial-opening thresholds (none, 30% of doses must be used, 60%) and MCV presentations (10-dose, 5-dose) on each supply chain. We linked these outputs to a clinical- and economic-outcomes model which translated the change in vaccine availability to associated infections, medical costs, and DALYs. We calculated the economic impact of each policy from the health system perspective.

The vial-opening threshold that maximizes vaccine availability while minimizing costs varies between individual countries. In Benin (median session size = 5), implementing a 30% vial-opening threshold and tailoring distribution of 10-dose and 5-dose MCVs to clinics based on session size is the most cost-effective policy, preventing 671 DALYs ($471/DALY averted) compared to baseline (no threshold, 10-dose MCVs). In Niger (median MCV session size = 9), setting a 60% vial-opening threshold and tailoring MCV presentations is the most cost-effective policy, preventing 2897 DALYs ($16.05/ DALY averted). In Mozambique (median session size = 3), setting a 30% vial-opening threshold using 10-dose MCVs is the only beneficial policy compared to baseline, preventing 3081 DALYs ($85.98/DALY averted). Across all three countries, however, a 30% vial-opening threshold using 10-dose MCVs everywhere is the only MCV threshold that consistently benefits each system compared to baseline. #### CONCLUSION: While the ideal vial-opening threshold policy for MCV varies by supply chain, implementing a 30% vial-opening threshold for 10-dose MCVs benefits each system by improving overall vaccine availability and reducing associated medical costs and DALYs compared to no threshold. The HIV research program at IDM provides analytical support to our research, policy, and implementation partners. These include estimates and forecasts of epidemic trends, as well as impact estimation for interventions that can be used to develop strategic plans, target product profiles, and field studies. To support these efforts, we have developed a very flexible individual-based modeling software tool, EMOD-HIV, for which source code and documentation are freely available online, and training is available on request both through IDM and our research collaborator network. Current priorities for our research agenda include: • Estimating demographic shifts in HIV burden and address these in resource-limited settings. • Estimating the impact of emerging interventions such as pre-exposure prophylaxis, HIV self-testing, community-based treatment, and point-of-care patient monitoring. Daniel Klein , Edinah Mudimu, Kathryn Peebles, Zindoga Mukandavire, Emily Nightingale, Monisha Sharma, Graham F. Medley, Daniel J. Klein, Katharine Kripke, Anna Bershteyn PLOS One Background Pre-exposure prophylaxis (PrEP) is highly effective in preventing HIV and has the potential to significantly impact the HIV epidemic. Given limited resources for HIV prevention, identifying PrEP provision strategies that maximize impact is critical. Methods We used a stochastic individual-based network model to evaluate the direct (infections prevented among PrEP users) and indirect (infections prevented among non-PrEP users as a result of PrEP) benefits of PrEP, the person-years of PrEP required to prevent one HIV infection, and the community-level impact of providing PrEP to populations defined by gender and age in western Kenya and South Africa. We examined sensitivity of results to scale-up of antiretroviral therapy (ART) and voluntary medical male circumcision (VMMC) by comparing two scenarios: maintaining current coverage (“status quo”) and rapid scale-up to meet programmatic targets (“fast-track”). Results The community-level impact of PrEP was greatest among women aged 15–24 due to high incidence, while PrEP use among men aged 15–24 yielded the highest proportion of indirect infections prevented in the community. These indirect infections prevented continue to increase over time (western Kenya: 0.4–5.5 (status quo); 0.4–4.9 (fast-track); South Africa: 0.5–1.8 (status quo); 0.5–3.0 (fast-track)) relative to direct infections prevented among PrEP users. The number of person-years of PrEP needed to prevent one HIV infection was lower (59 western Kenya and 69 in South Africa in the status quo scenario; 201 western Kenya and 87 in South Africa in the fast-track scenario) when PrEP was provided only to women compared with only to men over time horizons of up to 5 years, as the indirect benefits of providing PrEP to men accrue in later years. Conclusions Providing PrEP to women aged 15–24 prevents the greatest number of HIV infections per person-year of PrEP, but PrEP provision for young men also provides indirect benefits to women and to the community overall. This finding supports existing policies that prioritize PrEP use for young women, while also illuminating the community-level benefits of PrEP availability for men when resources permit. Adam Akullian , Monisha Sharma, PhD, Edinah Mudimu, PhD Kate Simeon, MD, Anna Bershteyn, PhD, Jienchi Dorward, MBChB, Lauren R Violette, MPH, Adam Akullian, PhD, Prof Salim S Abdool Karim, MBBCH, Prof Connie Celum, MD, Nigel Garrett, MBBS, Paul K Drain, MD The Lancet HIV Background The number of people on antiretroviral therapy (ART) requiring treatment monitoring in low-resource settings is rapidly increasing. Point-of-care (POC) testing for ART monitoring might alleviate burden on centralised laboratories and improve clinical outcomes, but its cost-effectiveness is unknown. Methods We used cost and effectiveness data from the STREAM trial in South Africa (February, 2017–October, 2018), which evaluated POC testing for viral load, CD4 count, and creatinine, with task shifting from professional to lower-cadre registered nurses compared with laboratory-based testing without task shifting (standard of care). We parameterised an agent-based network model, EMOD-HIV, to project the impact of implementing this intervention in South Africa over 20 years, simulating approximately 175 000 individuals per run. We assumed POC monitoring increased viral suppression by 9 percentage points, enrolment into community-based ART delivery by 25 percentage points, and switching to second-line ART by 1 percentage point compared with standard of care, as reported in the STREAM trial. We evaluated POC implementation in varying clinic sizes (10–50 patient initiating ART per month). We calculated incremental cost-effectiveness ratios (ICERs) and report the mean and 90% model variability of 250 runs, using a cost-effectiveness threshold of US$500 per disability-adjusted life-year (DALY) averted for our main analysis.

Findings
POC testing at 70% coverage of patients on ART was projected to reduce HIV infections by 4·5% (90% model variability 1·6 to 7·6) and HIV-related deaths by 3·9% (2·0 to 6·0). In clinics with 30 ART initiations per month, the intervention had an ICER of $197 (90% model variability –27 to 863) per DALY averted; results remained cost-effective when varying background viral suppression, ART dropout, intervention effectiveness, and reduction in HIV transmissibility. At higher clinic volumes (≥40 ART initiations per month), POC testing was cost-saving and at lower clinic volumes (20 ART initiations per month) the ICER was$734 (93 to 2569). A scenario that assumed POC testing did not increase enrolment into community ART delivery produced ICERs that exceeded the cost-effectiveness threshold for all clinic volumes.

Interpretation
POC testing is a promising strategy to cost-effectively improve patient outcomes in moderately sized clinics in South Africa. Results are most sensitive to changes in intervention impact on enrolment into community-based ART delivery.

Funding
National Institutes of Health.

Adam Akullian , Anna Bershteyn, Monisha Sharma, Adam Akullian, Kathryn Peebles, Supriya Sarkar, R Scott Braithwaite, Edinah Mudimu

Journal of the International AIDS Society

### Introduction

Over one hundred implementation studies of HIV pre‐exposure prophylaxis (PrEP) are completed, underway or planned. We synthesized evidence from these studies to inform mathematical modelling of the prevention cascade for oral and long‐acting PrEP in the setting of western Kenya, one of the world’s most heavily HIV‐affected regions.

### Methods

We incorporated steps of the PrEP prevention cascade – uptake, adherence, retention and re‐engagement after discontinuation – into EMOD‐HIV, an open‐source transmission model calibrated to the demography and HIV epidemic patterns of western Kenya. Early PrEP implementation research from East Africa was used to parameterize prevention cascades for oral PrEP as currently implemented, delivery innovations for oral PrEP, and future long‐acting PrEP. We compared infections averted by PrEP at the population level for different cascade assumptions and sub‐populations on PrEP. Analyses were conducted over the 2020 to 2040 time horizon, with additional sensitivity analyses for the time horizon of analysis and the time when long‐acting PrEP becomes available.

### Results

The maximum impact of oral PrEP diminished by over 98% across all prevention cascades, with the exception of long‐acting PrEP under optimistic assumptions about uptake and re‐engagement after discontinuation. Long‐acting PrEP had the highest population‐level impact, even after accounting for possible delays in product availability, primarily because its effectiveness does not depend on drug adherence. Retention was the most significant cascade step reducing the potential impact of long‐acting PrEP. These results were robust to assumptions about the sub‐populations receiving PrEP, but were highly influenced by assumptions about re‐initiation of PrEP after discontinuation, about which evidence was sparse.

### Conclusions

Implementation challenges along the prevention cascade compound to diminish the population‐level impact of oral PrEP. Long‐acting PrEP is expected to be less impacted by user uptake and adherence, but it is instead dependent on product availability in the short term and retention in the long term. To maximize the impact of long‐acting PrEP, ensuring timely product approval and rollout is critical. Research is needed on strategies to improve retention and patterns of PrEP re‐initiation.

Adam Akullian , Dan Bridenbecker , Adam Akullian , Michelle Morrison, Geoffrey P Garnett, Zandile Mnisi, Nomthandazo Lukhele, Daniel Bridenbecker, Anna Bershteyn

The Lancet HIV

### Background

The rapid scale-up of antiretroviral therapy (ART) towards the UNAIDS 90-90-90 goals over the last decade has sparked considerable debate as to whether universal test and treat can end the HIV-1 epidemic in sub-Saharan Africa. We aimed to develop a network transmission model, calibrated to capture age-specific and sex-specific gaps in the scale-up of ART, to estimate the historical and future effect of attaining and surpassing the UNAIDS 90-90-90 treatment targets on HIV-1 incidence and mortality, and to assess whether these interventions will be enough to achieve epidemic control (incidence of 1 infection per 1000 person-years) by 2030.

### Methods

We used eSwatini (formerly Swaziland) as a case study to develop our model. We used data on HIV prevalence by 5-year age bins, sex, and year from the 2007 Swaziland Demographic Health Survey (SDHS), the 2011 Swaziland HIV Incidence Measurement Survey, and the 2016 Swaziland Population Health Impact Assessment (PHIA) survey. We estimated the point prevalence of ART coverage among all HIV-infected individuals by age, sex, and year. Age-specific data on the prevalence of male circumcision from the SDHS and PHIA surveys were used as model inputs for traditional male circumcision and scale-up of voluntary medical male circumcision (VMMC). We calibrated our model using publicly available data on demographics; HIV prevalence by 5-year age bins, sex, and year; and ART coverage by age, sex, and year. We modelled the effects of five scenarios (historical scale-up of ART and VMMC [status quo], no ART or VMMC, no ART, age-targeted 90-90-90, and 100% ART initiation) to quantify the contribution of ART scale-up to declines in HIV incidence and mortality in individuals aged 15–49 by 2016, 2030, and 2050.

### Findings

Between 2010 and 2016, status-quo ART scale-up among adults (aged 15–49 years) in eSwatini (from 34·0% in 2010 to 74·1% in 2016) reduced HIV incidence by 43·57% (95% credible interval 39·71 to 46·36) and HIV mortality by 56·17% (54·06 to 58·92) among individuals aged 15–49 years, with larger reductions in incidence among men and mortality among women. Holding 2016 ART coverage levels by age and sex into the future, by 2030 adult HIV incidence would fall to 1·09 (0·87 to 1·29) per 100 person-years, 1·42 (1·13 to 1·71) per 100 person-years among women and 0·79 (0·63 to 0·94) per 100 person-years among men. Achieving the 90-90-90 targets evenly by age and sex would further reduce incidence beyond status-quo ART, primarily among individuals aged 15–24 years (an additional 17·37% [7·33 to 26·12] reduction between 2016 and 2030), with only modest additional incidence reductions in adults aged 35–49 years (1·99% [–5·09 to 7·74]). Achieving 100% ART initiation among all people living with HIV within an average of 6 months from infection—an upper bound of plausible treatment effect—would reduce adult HIV incidence to 0·73 infections (0·55 to 0·92) per 100 person-years by 2030 and 0·46 (0·33 to 0·59) per 100 person-years by 2050.

### Interpretation

Scale-up of ART over the last decade has already contributed to substantial reductions in HIV-1 incidence and mortality in eSwatini. Focused ART targeting would further reduce incidence, especially in younger individuals, but even the most aggressive treatment campaigns would be insufficient to end the epidemic in high-burden settings without a renewed focus on expanding preventive measures.

### Funding

Global Good Fund and the Bill & Melinda Gates Foundation.

Adam Akullian , Alain Vandormael, Adam Akullian, Mark Siedner, Tulio de Oliveira, Till Bärnighausen and Frank Tanser

Nature Communications

Over the past decade, there has been a massive scale-up of primary and secondary prevention services to reduce the population-wide incidence of HIV. However, the impact of these services on HIV incidence has not been demonstrated using a prospectively followed, population-based cohort from South Africa—the country with the world’s highest rate of new infections. To quantify HIV incidence trends in a hyperendemic population, we tested a cohort of 22,239 uninfected participants over 92,877 person-years of observation. We report a 43% decline in the overall incidence rate between 2012 and 2017, from 4.0 to 2.3 seroconversion events per 100 person-years. Men experienced an earlier and larger incidence decline than women (59% vs. 37% reduction), which is consistent with male circumcision scale-up and higher levels of female antiretroviral therapy coverage. Additional efforts are needed to get more men onto consistent, suppressive treatment so that new HIV infections can be reduced among women.

Adam Akullian , Carol Camlin, Adam Akullian, Torsten Neilands, Monica Getahun, Anna Bershteyn, Sarah Ssali, ElvinGeng, Monica Gandhi, Craig Cohen, Irene Maeri,  Patrick Eyul, Maya L.Petersen, Diane Havlir, Moses Kamya, Elizabeth Bukusi, Edwin Charlebois

Health &amp; Place

Mobility in sub-Saharan Africa links geographically-separate HIV epidemics, intensifies transmission by enabling higher-risk sexual behavior, and disrupts care. This population-based observational cohort study measured complex dimensions of mobility in rural Uganda and Kenya. Survey data were collected every 6 months beginning in 2016 from a random sample of 2308 adults in 12 communities across three regions, stratified by intervention arm, baseline residential stability and HIV status. Analyses were survey-weighted and stratified by sex, region, and HIV status. In this study, there were large differences in the forms and magnitude of mobility across regions, between men and women, and by HIV status.

We found that adult migration varied widely by region, higher proportions of men than women migrated within the past one and five years, and men predominated across all but the most localized scales of migration: a higher proportion of women than men migrated within county of origin. Labor-related mobility was more common among men than women, while women were more likely to travel for non-labor reasons. Labor-related mobility was associated with HIV positive status for both men and women, adjusting for age and region, but the association was especially pronounced in women. The forms, drivers, and correlates of mobility in eastern Africa are complex and highly gendered. An in-depth understanding of mobility may help improve implementation and address gaps in the HIV prevention and care continua.

Adam Akullian , Dylan Green, Brenda Kharono, Diana M. Tordoff, Adam Akullian, Anna Bershteyn, Michelle Morrison, Geoff Garnett, Ann Duerr, Paul Drain

BMC

### Background

Despite policies for universal HIV testing and treatment (UTT) regardless of CD4 count, there are still 1.8 million new HIV infections and 1 million AIDS-related deaths annually. The UNAIDS 90-90-90 goals target suppression of HIV viral load in 73% of all HIV-infected people worldwide by 2030. However, achieving these targets may not lead to expected reductions in HIV incidence if the remaining 27% (persons with unsuppressed viral load) are the drivers of HIV transmission through high-risk behaviors. We aim to conduct a systematic review and meta-analysis to understand the demographics, mobility, geographic distribution, and risk profile of adults who are not virologically suppressed in sub-Saharan Africa in the era of UTT.

### Methods

We will review the published and grey literature for study sources that contain data on demographic and behavioral strata of virologically suppressed and unsuppressed populations since 2014. We will search PubMed and Embase using four sets of search terms tailored to identify characteristics associated with virological suppression (or lack thereof) and each of the individual 90-90-90 goals. Record screening and data abstraction will be done independently and in duplicate. We will use random effects meta-regression analyses to estimate the distribution of demographic and risk features among groups not virologically suppressed and for each individual 90-90-90 goal.

### Discussion

The results of our review will help elucidate factors associated with failure to achieve virological suppression in sub-Saharan Africa, as well as factors associated with failure to achieve each of the 90-90-90 goals. These data will help quantify the population-level effects of current HIV treatment interventions to improve strategies for maximizing virological suppression and ending the HIV epidemic.

International Journal of Health Geographics

### Background

Large geographical variations in the intensity of the HIV epidemic in sub-Saharan Africa call for geographically targeted resource allocation where burdens are greatest. However, data available for mapping the geographic variability of HIV prevalence and detecting HIV ‘hotspots’ is scarce, and population-based surveillance data are not always available. Here, we evaluated the viability of using clinic-based HIV prevalence data to measure the spatial variability of HIV in South Africa and Tanzania.

### Methods

Population-based and clinic-based HIV data from a small HIV hyper-endemic rural community in South Africa as well as for the country of Tanzania were used to map smoothed HIV prevalence using kernel interpolation techniques. Spatial variables were included in clinic-based models using co-kriging methods to assess whether cofactors improve clinic-based spatial HIV prevalence predictions. Clinic- and population-based smoothed prevalence maps were compared using partial rank correlation coefficients and residual local indicators of spatial autocorrelation.

### Results

Routinely-collected clinic-based data captured most of the geographical heterogeneity described by population-based data but failed to detect some pockets of high prevalence. Analyses indicated that clinic-based data could accurately predict the spatial location of so-called HIV ‘hotspots’ in > 50% of the high HIV burden areas.

### Conclusion

Clinic-based data can be used to accurately map the broad spatial structure of HIV prevalence and to identify most of the areas where the burden of the infection is concentrated (HIV ‘hotspots’). Where population-based data are not available, HIV data collected from health facilities may provide a second-best option to generate valid spatial prevalence estimates for geographical targeting and resource allocation.

Adam Akullian , Carol S Camlin, Adam Akullian, Torsten B Neilands,  Monica Getahun,  Patrick Eyul,  Irene Maeri, Sarah Ssali,  Elvin Geng,  Monica Gandhi,  Craig R Cohen,  Moses R Kamya,  Thomas Odeny, Elizabeth A Bukusi,  Edwin D Charlebois

Journal of the International AIDS Society

### Introduction

There are significant knowledge gaps concerning complex forms of mobility emergent in sub‐Saharan Africa, their relationship to sexual behaviours, HIV transmission, and how sex modifies these associations. This study, within an ongoing test‐and‐treat trial (SEARCH, NCT01864603), sought to measure effects of diverse metrics of mobility on behaviours, with attention to gender.

### Methods

Cross‐sectional data were collected in 2016 from 1919 adults in 12 communities in Kenya and Uganda, to examine mobility (labour/non‐labour‐related travel), migration (changes of residence over geopolitical boundaries) and their associations with sexual behaviours (concurrent/higher risk partnerships), by region and sex. Multilevel mixed‐effects logistic regression models, stratified by sex and adjusted for clustering by community, were fitted to examine associations of mobility with higher‐risk behaviours, in past 2 years/past 6 months, controlling for key covariates.

### Results

The population was 45.8% male and 52.4% female, with mean age 38.7 (median 37, IQR: 17); 11.2% had migrated in the past 2 years. Migration varied by region (14.4% in Kenya, 11.5% in southwestern and 1.7% in eastern and Uganda) and sex (13.6% of men and 9.2% of women). Ten per cent reported labour‐related travel and 45.9% non‐labour‐related travel in past 6 months—and varied by region and sex: labour‐related mobility was more common in men (18.5%) than women (2.9%); non‐labour‐related mobility was more common in women (57.1%) than men (32.6%). In 2015 to 2016, 24.6% of men and 6.6% of women had concurrent sexual partnerships; in past 6 months, 21.6% of men and 5.4% of women had concurrent partnerships. Concurrency in 2015 to 2016 was more strongly associated with migration in women [aRR = 2.0, 95% CI(1.1 to 3.7)] than men [aRR = 1.5, 95% CI(1.0 to 2.2)]. Concurrency in past 6 months was more strongly associated with labour‐related mobility in women [aRR = 2.9, 95% CI(1.0 to 8.0)] than men [aRR = 1.8, 95% CI(1.2 to 2.5)], but with non‐labour‐related mobility in men [aRR = 2.2, 95% CI(1.5 to 3.4)].

### Conclusions

In rural eastern Africa, both longer‐distance/permanent, and localized/shorter‐term forms of mobility are associated with higher‐risk behaviours, and are highly gendered: the HIV risks associated with mobility are more pronounced for women. Gender‐specific interventions among mobile populations are needed to combat HIV in the region.

Adam Akullian , Daniel Klein , Anna Bershteyn, Kennedy K Mutai, Adam Akullian, Daniel J Klein, Britta L Jewell, Samuel M Mwalili

Science Direct

Western Kenya suffers a highly endemic and also very heterogeneous epidemic of human immunodeficiency virus (HIV). Although female sex workers (FSW) and their male clients are known to be at high risk for HIV, HIV prevalence across regions in Western Kenya is not strongly correlated with the fraction of women engaged in commercial sex. An agent-based network model of HIV transmission, geographically stratified at the county level, was fit to the HIV epidemic, scale-up of interventions, and populations of FSW in Western Kenya under two assumptions about the potential mobility of FSW clients. In the first, all clients were assumed to be resident in the same geographies as their interactions with FSW. In the second, some clients were considered non-resident and engaged only in interactions with FSW, but not in longer-term non-FSW partnerships in these geographies. Under both assumptions, the model successfully reconciled disparate geographic patterns of FSW and HIV prevalence. Transmission patterns in the model suggest a greater role for FSW in local transmission when clients were resident to the counties, with 30.0% of local HIV transmissions attributable to current and former FSW and clients, compared to 21.9% when mobility of clients was included. Nonetheless, the overall epidemic drivers remained similar, with risky behavior in the general population dominating transmission in high-prevalence counties. Our modeling suggests that co-location of high-risk populations and generalized epidemics can further amplify the spread of HIV, but that large numbers of formal FSW and clients are not required to observe or mechanistically explain high HIV prevalence in the general population.

Adam Akullian , Adam Akullian, Bershteyn, Anna, Jewell, Britta, Camlin, Carol S.

AIDS

Though a wide body of observational and model-based evidence underscores the promise of Universal Test and Treat (UTT) to reduce population-level HIV incidence in high-burden areas of Sub-Saharan Africa (SSA), the only cluster- randomized trial of UTT completed to date, ANRS 12249, did not show a significant reduction in incidence. More UTT trials are currently underway, and some have already exceeded the Joint United Nations Programme on HIV/AIDS (UNAIDS) 90–90–90 targets. Still, even with high test and treat coverage, it is unknown whether ongoing trials will engage populations with the greatest potential for onward transmission to achieve the ambitious goal of reducing new HIV infections by 90% between 2010 and 2013. Ultimately, even strategies that successfully meet or exceed the 90– 90–90 targets will leave up to 27% of people living with HIV/AIDS virally nonsuppressed. The epidemiological profile of the ‘missing 27%’ – including their risk behavior, mobility, and network connectedness – is not well understood and must be better characterized to fully evaluate the effectiveness of UTT.

Scientific Reports

Under the premise that in a resource-constrained environment such as Sub-Saharan Africa it is not possible to do everything, to everyone, everywhere, detailed geographical knowledge about the HIV epidemic becomes essential to tailor programmatic responses to specific local needs. However, the design and evaluation of national HIV programs often rely on aggregated national level data. Against this background, here we proposed a model to produce high-resolution maps of intranational estimates of HIV prevalence in Kenya, Malawi, Mozambique and Tanzania based on spatial variables. The HIV prevalence maps generated highlight the stark spatial disparities in the epidemic within a country, and localize areas where both the burden and drivers of the HIV epidemic are concentrated. Under an era focused on optimal allocation of evidence-based interventions for populations at greatest risk in areas of greatest HIV burden, as proposed by the Joint United Nations Programme on HIV/AIDS (UNAIDS) and the United States President’s Emergency Plan for AIDS Relief (PEPFAR), such maps provide essential information that strategically targets geographic areas and populations where resources can achieve the greatest impact.

Adam Akullian , Daniel Klein , Adam Akullian, Anna Bershteyn, Daniel Klein, Alain Vandormael, Till Barnighausen, and Frank Tanser

AIDS

Objective
To quantify the contribution of specific sexual partner age groups to the risk of HIV acquisition in men and women in hyperendemic region of South Africa.

Design
We conducted a population-based cohort study among women (15–49 years of age) and men (15–55 years of age) between 2004 and 2015 in KwaZulu-Natal, South Africa.

Methods:
Generalized additive models were used to estimate smoothed HIV incidence rates across partnership age pairings in men and women. Cox proportional hazards regression was used to estimate the relative risk of HIV acquisition by partner age group.

Results
A total of 882 HIV seroconversions were observed in 15 935 person-years for women, incidence rate¼5.5 per 100 person-years [95% confidence interval (CI), 5.2– 5.9] and 270 HIV seroconversions were observed in 9372 person-years for men, incidence rate¼2.9 per 100 person-years (95% CI, 2.6–3.2). HIV incidence was highest among 15–24-year-old women reporting partnerships with 30–34-year-old men, incidence rate¼9.7 per 100 person-years (95% CI, 7.2–13.1). Risk of HIV acquisition in women was associated with male partners aged 25–29 years (adjusted hazard ratio; aHR¼1.44, 95% CI, 1.02–2.04) and 30–34 years (aHR¼1.50, 95% CI, 1.08–2.09) relative to male partners aged 35 and above. Risk of HIV acquisition in men was associated with 25–29-year-old (aHR¼1.72, 95% CI, 1.02–2.90) and 30–34- year-old women (aHR¼2.12, 95% CI, 1.03–4.39) compared to partnerships with women aged 15–19 years.

Adam Akullian , Daniel Klein , Akullian, Adam PhD, Onyango, Mathews MPH, Klein, Daniel PhD, Odhiambo, Jacob MBChB, Bershteyn, Anna PhD

Medicine

Voluntary Medical Male Circumcision (VMMC) for human immunodeficiency virus (HIV) prevention has scaled up rapidly among young men in western Kenya since 2008. Whether the program has successfully reached uncircumcised men evenly across the region is largely unknown. Using data from two cluster randomized surveys from the 2008 and 2014 Kenyan Demographic Health Survey (KDHS), we mapped the continuous spatial distribution of circumcised men by age group across former Nyanza Province to identify geographic areas where local circumcision prevalence is lower than the overall, regional prevalence. The prevalence of self-reported circumcision among men 15 to 49 across six counties in former Nyanza Province increased from 45.6% (95% CI = 33.2–58.0%) in 2008 to 71.4% (95% CI = 67.4–75.0%) in 2014, with the greatest increase in men 15 to 24 years of age, from 40.4% (95% CI = 27.7–55.0%) in 2008 to 81.6% (95% CI = 77.2–85.0%) in 2014. Despite the dramatic scale-up of VMMC in western Kenya, circumcision coverage in parts of Kisumu, Siaya, and Homa Bay counties was lower than expected (P < 0.05), with up to 50% of men aged 15 to 24 still uncircumcised by 2014 in some areas. The VMMC program has proven successful in reaching a large population of uncircumcised men in western Kenya, but as of 2014, pockets of low circumcision coverage still existed. Closing regional gaps in VMMC prevalence to reach 80% coverage may require targeting specific areas where VMMC prevalence is lower than expected.

Daniel Klein , Anna Bershteyn, Daniel J. Klein, Philip A. Eckhoff

International Health

Background Generalized HIV epidemics propagate to future generations according to the age patterns of transmission. We hypothesized that future generations could be protected from infection using age-targeted prevention, analogous to the ring-fencing strategies used to control the spread of smallpox.

Methods We modeled age-targeted or cohort-targeted outreach with HIV treatment and/or prevention using EMOD-HIV v0·8, an individual-based network model of HIV transmission in South Africa.

Results Targeting ages 20 to 30 with intensified outreach, linkage, and eligibility for antiretroviral therapy (ART) averted 45% as many infections as universal outreach for approximately one-fifth the cost beyond existing HIV services. Though cost-effective, targeting failed to eliminate all infections to those under 20 due to vertical and inter-generational transmission. Cost-effectiveness of optimal prevention strategies included US$6238 per infection averted targeting ages 10–30, US$5031 targeting 20–30, US$4279 targeting 22–27, and US$3967 targeting 25–27, compared to US$10 812 for full-population test-and-treat. Minimizing burden (disability-adjusted life years [DALYs]) rather than infections resulted in older target age ranges because older adults were more likely to receive a direct health benefit from treatment. Conclusions Age-targeted treatment for HIV prevention is unlikely to eliminate HIV epidemics, but is an efficient strategy for reducing new infections in generalized epidemics settings. Adam Akullian , Adam M Akullian, Aggrey Mukose, Gillian A Levine, Joseph B Babigumira Journal of the International AIDS Society ### Introduction The availability of specialized HIV services is limited in rural areas of sub-Saharan Africa where the need is the greatest. Where HIV services are available, people living with HIV (PLHIV) must overcome large geographic, economic and social barriers to access healthcare. The objective of this study was to understand the unique barriers PLHIV face when accessing healthcare compared with those not living with HIV in a rural area of sub-Saharan Africa with limited availability of healthcare infrastructure. ### Methods We conducted a population-based cross-sectional study of 447 heads of household on Bugala Island, Uganda. Multiple linear regression models were used to compare travel time, cost and distance to access healthcare, and log binomial models were used to test for associations between HIV status and access to nearby health services. ### Results PLHIV travelled an additional 1.9 km (95% CI (0.6, 3.2 km), p=0.004) to access healthcare compared with those not living with HIV, and they were 56% less likely to access healthcare at the nearest health facility to their residence, so long as that facility lacked antiretroviral therapy (ART) services (aRR=0.44, 95% CI (0.24 to 0.83), p=0.011). We found no evidence that PLHIV travelled further for care if the nearest facility supplies ART services (aRR=0.95, 95% CI (0.86 to 1.05), p=0.328). Among those who reported uptake of care at one of two facilities on the island that provides ART (81% of PLHIV and 68% of HIV-negative individuals), PLHIV tended to seek care at a higher tiered facility that provides ART, even when this facility was not their closest facility (30% of PLHIV travelled further than the closest ART facility compared with 16% of HIV-negative individuals), and travelled an additional 2.2 km (p=0.001) to access that facility, relative to HIV-negative individuals (aRR=1.91, 95% CI (1.00 to 3.65), p=0.05). Among PLHIV, residential distance was associated with access to facilities providing ART (RR=0.78, 95% CI (0.61 to 0.99), p=0.044, comparing residential distances of 3–5 km to 0–2 km; RR=0.71, 95% CI (0.58 to 0.87), p=0.001, comparing residential distances of 6–10 km to 0–2 km). ### Conclusions PLHIV travel longer distances for care, a phenomenon that may be driven by both the limited availability of specialized HIV services and preference for higher tiered facilities. Daniel Klein , Dr Jeffrey W Eaton, Nicolas Bacaër, PhD, Anna Bershteyn, PhD, Valentina Cambiano, PhD, Anne Cori, PhD, Prof Rob E Dorrington, MPhil, Prof Christophe Fraser, PhD, Chaitra Gopalappa, PhD, Jan A C Hontelez, PhD, Leigh F Johnson, PhD, Daniel J Klein, PhD, Prof Andrew N Phillips, PhD, Carel Pretorius, PhD, John Stover, MA, Prof Thomas M Rehle, MD, Prof Timothy B Hallett, PhD The Lancet Global Health ### Background Mathematical models are widely used to simulate the effects of interventions to control HIV and to project future epidemiological trends and resource needs. We aimed to validate past model projections against data from a large household survey done in South Africa in 2012. ### Methods We compared ten model projections of HIV prevalence, HIV incidence, and antiretroviral therapy (ART) coverage for South Africa with estimates from national household survey data from 2012. Model projections for 2012 were made before the publication of the 2012 household survey. We compared adult (age 15–49 years) HIV prevalence in 2012, the change in prevalence between 2008 and 2012, and prevalence, incidence, and ART coverage by sex and by age groups between model projections and the 2012 household survey. ### Findings All models projected lower prevalence estimates for 2012 than the survey estimate (18·8%), with eight models' central projections being below the survey 95% CI (17·5–20·3). Eight models projected that HIV prevalence would remain unchanged (n=5) or decline (n=3) between 2008 and 2012, whereas prevalence estimates from the household surveys increased from 16·9% in 2008 to 18·8% in 2012 (difference 1·9, 95% CI −0·1 to 3·9). Model projections accurately predicted the 1·6 percentage point prevalence decline (95% CI −0·3 to 3·5) in young adults aged 15–24 years, and the 2·2 percentage point (0·5 to 3·9) increase in those aged 50 years and older. Models accurately represented the number of adults on ART in 2012; six of ten models were within the survey 95% CI of 1·54–2·12 million. However, the differential ART coverage between women and men was not fully captured; all model projections of the sex ratio of women to men on ART were lower than the survey estimate of 2·22 (95% CI 1·73–2·71). ### Interpretation Projections for overall declines in HIV epidemics during the ART era might have been optimistic. Future treatment and HIV prevention needs might be greater than previously forecasted. Additional data about service provision for HIV care could help inform more accurate projections. ### Funding Bill & Melinda Gates Foundation. Daniel Klein , Gesine Meyer-Rath, Mead Over, Dan Klein, Anna Bershteyn, The Center for Global Development The South African government is currently discussing various alternative approaches to the further expansion of antiretroviral treatment (ART) in public-sector facilities. Alternatives under consideration include the criteria under which a patient would be eligible for free care, the level of coverage with testing and care, how much of the care will be delivered in small facilities located closer to the patients, and how to assure linkage to care and subsequent adherence by ART patients. We used the EMOD-HIV model to generate 12 epidemiological scenarios. The EMOD-HIV model is a model of HIV transmission which projects South African HIV incidence and prevalence and ARV treatment by age group for alternative combinations of treatment eligibility criteria and testing. We treat as sunk costs the projected future cost of one of these 12 scenarios, the baseline scenario characterizing South Africa’s 2013 policy to treat people with CD4 counts less than 350. We compute the cost and benefits of the other 11 scenarios relative to this baseline. Starting with our own bottom-up cost analyses in South Africa, we separate outpatient cost into non-scale-dependent costs (drugs and laboratory tests) and scale-dependent cost (staff, space, equipment and overheads) and model the cost of production according to the expected future number and size of clinics. On the demand side, we include the cost of creating and sustaining the projected incremental demand for testing and treatment. Previous research with EMOD-HIV has shown that more vigorous recruitment of patients with CD4 counts less than 350 appears to be an advantageous policy over a five-year horizon. Over 20 years, however, the model assumption that a person on treatment is 92 percent less infectious improves the cost-effectiveness of higher eligibility thresholds over more vigorous recruitment at the lower threshold of 350, averting HIV infections for between$1,700 and $2,800 (under our central assumptions), while more vigorous expansion under the current guidelines would cost more than$7,500 per incremental HIV infection averted.

Granular spatial models of demand and cost facilitate the optimal targeting of new facility construction and outreach services. Based on analysis of the sensitivity of the results to 1,728 alternative parameter combinations at each of four discount rates, we conclude that better knowledge of the behavioral elasticities would be valuable, reducing the uncertainty of cost estimates by a factor of 4 to 10.

Daniel Klein , Daniel J. Klein, Philip A. Eckhoff, Anna Bershteyn

International Health

Background

Migrant populations such as mine workers contributed to the spread of HIV in sub-Saharan Africa. We used a mathematical model to estimate the community-wide impact of targeting treatment and prevention to male migrants.

Methods

We augmented an individual-based network model, EMOD-HIV v0.8, to include an age-dependent propensity for males to migrate. Migrants were exposed to HIV outside their home community, but continued to participate in HIV transmission in the community during periodic visits.

Results

Migrant-targeted interventions would have been transformative in the 1980s to 1990s, but post-2015 impacts were more modest. When targetable migrants comprised 2% of adult males, workplace HIV prevention averted 3.5% of community-wide infections over 20 years. Targeted treatment averted 8.5% of all-cause deaths among migrants. When migrants comprised 10% of males, workplace prevention averted 16.2% of infections in the community, one-quarter of which were among migrants. Workplace prevention and treatment acted synergistically, averting 17.1% of community infections and 11.6% of deaths among migrants. These estimates do not include prevention of secondary spread of HIV or tuberculosis at the workplace.

Conclusions

Though cost-effective, targeting migrants cannot collapse generalized epidemics in their home communities. Such a strategy would only have been possible prior to the early 1990s. However, migrant-targeted interventions synergize with general-population expansion of HIV services.

Daniel Klein , Stewart Chang , Bradley Wagner , Jeffrey W Eaton, PhD†, Nicolas A Menzies, MPH†, John Stover, MA, Valentina Cambiano, MS, Leonid Chindelevitch, PhD, Anne Cori, PhD, Jan A C Hontelez, PhD, Salal Humair, PhD, Cliff C Kerr, PhD, Daniel Klein, PhD, Sharmistha Mishra, MD, Kate M Mitchell, PhD, Brooke E Nichols, MS, Prof Peter Vickerman, DPhil, Roel Bakker, PhD, Till Bärnighausen, DSc, Anna Bershteyn, PhD, Prof David E Bloom, PhD, Marie-Claude Boily, PhD, Stewart T Chang, PhD, Ted Cohen, DPH, Peter J Dodd, PhD, Prof Christophe Fraser, PhD, Chaitra Gopalappa, PhD, Prof Jens Lundgren, DMSc, Natasha K Martin, DPhil, Evelinn Mikkelsen, MSc, Elisa Mountain, MSc, Quang D Pham, MD, Michael Pickles, PhD, Prof Andrew Phillips, PhD, Lucy Platt, PhD, Carel Pretorius, PhD, Holly J Prudden, MSc, Prof Joshua A Salomon, PhD, David A M C van de Vijver, PhD, Sake J de Vlas, PhD, Bradley G Wagner, PhD, Richard G White, PhD, David P Wilson, PhD, Lei Zhang, PhD, John Blandford, PhD, Gesine Meyer-Rath, PhD, Michelle Remme, MSc, Paul Revill, PhD, Nalinee Sangrujee, PhD, Fern Terris-Prestholt, PhD, Meg Doherty, PhD, Nathan Shaffer, MD, Prof Philippa J Easterbrook, MD, Gottfried Hirnschall, MD, Prof Timothy B Hallett, PhD

The Lancet Global Health

Background: New WHO guidelines recommend initiation of antiretroviral therapy for HIV-positive adults with CD4 counts of 500 cells per μL or less, a higher threshold than was previously recommended. Country decision makers have to decide whether to further expand eligibility for antiretroviral therapy accordingly. We aimed to assess the potential health benefits, costs, and cost-effectiveness of various eligibility criteria for adult antiretroviral therapy and expanded treatment coverage.

### Findings

#### CONCLUSION:

While the ideal vial-opening threshold policy for MCV varies by supply chain, implementing a 30% vial-opening threshold for 10-dose MCVs benefits each system by improving overall vaccine availability and reducing associated medical costs and DALYs compared to no threshold.

The emergent pathogen research program at IDM provides support to pandemic-preparedness and outbreak-response partners through data analysis, dynamical modeling, and genetic inference. Focus areas include recent outbreaks of Ebola, sylvatic reservoirs of vector-borne viruses, and transmission characteristics of seasonal flu.

Our Ebola research centers on characterizing the geographical spread of disease at different scales -- household, neighborhood, village, regional -- and relating to genetic and case-report data. The work elucidates the role of population sub-structure and the impact of social mobilization, behavior change, isolation facilities, and vaccination strategies. The goal is to provide timely support to operational and strategic partners in ongoing outbreaks.

Our influenza research targets improved pandemic preparedness through a more detailed understanding of the regional transmission characteristics of seasonal flu -- importation, spatial connectivity, and contact patterns (household, workplace, schools). Through our involvement in the Seattle Flu Study -- including geo-statistical modeling and phylogenetic inference -- our goal is to advance the real-time awareness of disease dynamics and to demonstrate the potential of novel diagnostic and intervention strategies.

Some areas of work include:

• Role of Monkeys in Sylvatic Cycle of Chikungunya.
• Potential for Zika Virus to Establish a Sylvatic Cycle in the Americas.
• Identifying Spatiotemporal Dynamics of Ebola in Sierra Leone Using Virus Genomes.

Navideh Noori , Mollie Van Gordon , Brittany Hagedorn , Ben Althouse , Edward Wenger , Andre Lin Ouedraogo , Laura Skrip, Karim Derra, Mikaila Kaboré, Navideh Noori, Adama Gansané, Innocent Valéa, Halidou Tinto, Bicaba W. Brice, Mollie Van Gordon, Brittany Hagedorn, Hervé Hien, Benjamin M. Althouse, Edward A. Wenger, André Lin Ouédraogo

International Journal of Infectious Diseases

### Background

Absolute numbers of COVID-19 cases and deaths reported to date in the sub-Saharan Africa (SSA) region have been significantly lower than those across the Americas, Asia, and Europe. As a result, there has been limited information about the demographic and clinical characteristics of deceased cases in the region, as well as the impacts of different case management strategies.

### Methods

Data from deceased cases reported across SSA through May 10, 2020 and from hospitalized cases in Burkina Faso through April 15, 2020 were analyzed. Demographic, epidemiological, and clinical information on deceased cases in SSA was derived through a line-list of publicly available information and, for cases in Burkina Faso, from aggregate records at the Centre Hospitalier Universitaire de Tengandogo in Ouagadougou. A synthetic case population was derived probabilistically using distributions of age, sex, and underlying conditions from populations of West African countries to assess individual risk factors and treatment effect sizes. Logistic regression analysis was conducted to evaluate the adjusted odds of survival for patients receiving oxygen therapy or convalescent plasma, based on therapeutic effectiveness observed for other respiratory illnesses.

### Results

Across SSA, deceased cases for which demographic data are available have been predominantly male (63/103, 61.2%) and over 50 years of age (59/75, 78.7%). In Burkina Faso, specifically, the majority of deceased cases either did not seek care at all or were hospitalized for a single day (59.4%, 19/32); hypertension and diabetes were often reported as underlying conditions. After adjustment for sex, age, and underlying conditions in the synthetic case population, the odds of mortality for cases not receiving oxygen therapy was significantly higher than those receiving oxygen, such as due to disruptions to standard care (OR: 2.07; 95% CI: 1.56 – 2.75). Cases receiving convalescent plasma had 50% reduced odds of mortality than those who did not (95% CI: 0.24 – 0.93).

### Conclusions

Investment in sustainable production and maintenance of supplies for oxygen therapy, along with messaging around early and appropriate use for healthcare providers, caregivers, and patients could reduce COVID-19 deaths in SSA. Further investigation into convalescent plasma is warranted, as data on its effectiveness specifically in treating COVID-19 becomes available. The success of supportive or curative clinical interventions will depend on earlier treatment seeking, such that community engagement and risk communication will be critical components of the response.

Ben Althouse , Laura A Skrip PhD, Jamie Bedson MSSc, Sharon Abramowitz PhD, Mohammed B Jalloh MPH, Saiku Bah MSc, Mohamed F Jalloh MPH, Ollin Demian Langle-Chimal MSc, Nicholas Cheney PhD, LaurentHébert-Dufresne PhD, Benjamin M Althouse PhD

The Lancet Planetary Health

### Background

The west African Ebola epidemic (2014–15) necessitated behaviour change in settings with prevalent and pre-existing unmet needs as well as extensive mechanisms for local community action. We aimed to assess spatial and temporal trends in community-reported needs and associations with behaviour change, community engagement, and the overall outbreak situation in Sierra Leone.

### Methods

We did a retrospective, mixed-methods study. Post-hoc analyses of data from 12 096 mobiliser visits as part of the Social Mobilization Action Consortium were used to describe the evolution of satisfied and unsatisfied needs (basic, security, autonomy, respect, and social support) between Nov 12, 2014, and Dec 18, 2015, and across 14 districts. Via Bayesian hierarchical regression modelling, we investigated associations between needs categories and behaviours (numbers of individuals referred to treatment within 24 h of symptom onset or deaths responded to with safe and dignified burials) and the role of community engagement programme status (initial vs follow-up visit) in the association between satisfied versus unsatisfied needs and behaviours.

### Findings

In general, significant associations were observed between unsatisfied needs categories and both prompt referrals to treatment and safe burials. Most notably, communities expressing unsatisfied capacity needs reported fewer safe burials (relative risk [RR] 0·86, 95% credible interval [CrI] 0·82–0·91) and fewer prompt referrals to treatment (RR 0·76, 0·70–0·83) than did those without unsatisfied capacity needs. The exception was expression of unsatisfied basic needs, which was associated with significantly fewer prompt referrals only (RR 0·86, 95% CrI 0·79–0·93). Compared with triggering visits by community mobilisers, follow-up visits were associated with higher numbers of prompt referrals (RR 1·40, 95% CrI 1·30–1·50) and safe burials (RR 1·08, 1·02–1·14).

### Interpretation

Community-based development of locally feasible, locally owned action plans, with the support of community mobilisers, has potential to address unmet needs for more sustained behaviour change in outbreak settings.

### Funding

Bill & Melinda Gates, Bill & Melinda Gates Foundation, and National Institutes of Health.

Ben Althouse , Benjamin M Althouse, Samuel V Scarpino, Lauren Ancel Meyers, John W Ayers, Marisa Bargsten, Joan Baumbach, John S Brownstein, Lauren Castro, Hannah Clapham, Derek AT Cummings, Sara Del Valle, Stephen Eubank, Geoffrey Fairchild, Lyn Finelli, Nicholas Generous, Dylan George, David R Harper, Laurent Hébert-Dufresne, Michael A Johansson, Kevin Konty, Marc Lipsitch, Gabriel Milinovich, Joseph D Miller, Elaine O Nsoesie, Donald R Olson, Michael Paul, Philip M Polgreen, Reid Priedhorsky, Jonathan M Read, Isabel Rodríguez-Barraquer, Derek J Smith, Christian Stefansen, David L Swerdlow, Deborah Thompson, Alessandro Vespignani and Amy Wesolowski

EPJ Data Science

Novel data streams (NDS), such as web search data or social media updates, hold promise for enhancing the capabilities of public health surveillance. In this paper, we outline a conceptual framework for integrating NDS into current public health surveillance. Our approach focuses on two key questions: What are the opportunities for using NDS and what are the minimal tests of validity and utility that must be applied when using NDS? Identifying these opportunities will necessitate the involvement of public health authorities and an appreciation of the diversity of objectives and scales across agencies at different levels (local, state, national, international). We present the case that clearly articulating surveillance objectives and systematically evaluating NDS and comparing the performance of NDS to existing surveillance data and alternative NDS data is critical and has not sufficiently been addressed in many applications of NDS currently in the literature.

Poliomyelitis “polio” is an acute, viral, infectious disease spread from person to person primarily through contact with the contaminated stool of an infected person. According to the World Health Organization (WHO), 1 in 200 polio infections will result in permanent paralysis especially in children younger than 5 years old, who are the most likely to contract the virus. Although there is no cure, polio can be prevented through vaccination. Since the 1980s, vaccination efforts have reduced the polio burden by 99.9% from 350,00 cases in 1988 to 22 reported cases in 2017. With the help of organizations such as the WHO, U.S Centers for Disease control and Prevention, UNICEF, and the Bill and Melinda Gates Foundation more than 16 million children have been saved from paralysis thus ensuring that 80% of the world’s population now lives in polio-free regions. However, polio still exists in some of the world’s most complex regions, notably Afghanistan, Pakistan, and Nigeria, and until the number of cases reported equates to zero, the fight for eradication will not stop.

Our Mission

Our aim is to support polio eradication efforts from the sub-national to the global level by doing the following:

• Conducting policy-based research and computer simulations.
• Using advanced analytics and disease transmission models to project the impact of the strategies currently being used to fight the disease.
• Evaluate the impact that novel strategies could have before they are rolled out to the field.

http://www.who.int/topics/poliomyelitis/en/

Steve Kroiss , Guillaume Chabot-Couture , Mike Famulare , Kevin McCarthy , Hil Lyons , Steve J. Kroiss, Maiwand Ahmadzai, Jamal Ahmed, Muhammad Masroor Alam, Guillaume Chabot-Couture, Michael Famulare, Abdirahman Mahamud, Kevin A. McCarthy, Laina D. Mercer, Salman Muhammad, Rana M. Safdar, Salmaan Sharif, Shahzad Shaukat, Hemant Shukla, Hil Lyons

PLOS One

The polio environmental surveillance (ES) system has been an incredible tool for advancing polio eradication efforts because of its ability to highlight the spatial and temporal extent of poliovirus circulation. While ES often outperforms, or is more sensitive than AFP surveillance, the sensitivity of the ES system has not been well characterized. Fundamental uncertainty of ES site sensitivity makes it difficult to interpret results from ES, particularly negative results.

Mike Famulare , Kevin McCarthy , Guillaume Chabot-Couture , Michael Famulare, Christian Selinger, Kevin A. McCarthy, Philip A. Eckhoff, Guillaume Chabot-Couture

PLoS Biol. 2018

The oral polio vaccine (OPV) contains live-attenuated polioviruses that induce immunity by causing low virulence infections in vaccine recipients and their close contacts. Widespread immunization with OPV has reduced the annual global burden of paralytic poliomyelitis by a factor of 10,000 or more and has driven wild poliovirus (WPV) to the brink of eradication. However, in instances that have so far been rare, OPV can paralyze vaccine recipients and generate vaccine-derived polio outbreaks. To complete polio eradication, OPV use should eventually cease, but doing so will leave a growing population fully susceptible to infection. If poliovirus is reintroduced after OPV cessation, under what conditions will OPV vaccination be required to interrupt transmission? Can conditions exist in which OPV and WPV reintroduction present similar risks of transmission? To answer these questions, we built a multi-scale mathematical model of infection and transmission calibrated to data from clinical trials and field epidemiology studies. At the within-host level, the model describes the effects of vaccination and waning immunity on shedding and oral susceptibility to infection. At the between-host level, the model emulates the interaction of shedding and oral susceptibility with sanitation and person-to-person contact patterns to determine the transmission rate in communities. Our results show that inactivated polio vaccine (IPV) is sufficient to prevent outbreaks in low transmission rate settings and that OPV can be reintroduced and withdrawn as needed in moderate transmission rate settings. However, in high transmission rate settings, the conditions that support vaccine-derived outbreaks have only been rare because population immunity has been high. Absent population immunity, the Sabin strains from OPV will be nearly as capable of causing outbreaks as WPV. If post-cessation outbreak responses are followed by new vaccine-derived outbreaks, strategies to restore population immunity will be required to ensure the stability of polio eradication.

Steve Kroiss , Hil Lyons , Guillaume Chabot-Couture , Laina D. Mercer, Rana M. Safdar, Jamal Ahmed, Abdirahman Mahamud, M. Muzaffar Khan, Sue Gerber, Aiden O’Leary, Mike Ryan, Frank Salet, Steve J. Kroiss, Hil Lyons, Alexander Upfill-Brown, and Guillaume Chabot-Couture

BMC Medicine

### Background

Pakistan is one of only three countries where poliovirus circulation remains endemic. For the Pakistan Polio Eradication Program, identifying high risk districts is essential to target interventions and allocate limited resources.

### Methods

Using a hierarchical Bayesian framework we developed a spatial Poisson hurdle model to jointly model the probability of one or more paralytic polio cases, and the number of cases that would be detected in the event of an outbreak. Rates of underimmunization, routine immunization, and population immunity, as well as seasonality and a history of cases were used to project future risk of cases.

### Results

AFP surveillance in Pakistan collected data on 43,301 NPAFP cases between January 2003 and June 2016, with an average annual rate increasing from 4.3 to 11.4 NPAFP per 100,000 children under the age of 5 years from 2003 to 2016. Space–time smoothing models fit to the NPAFP vaccination dose history data indicated that zero dose RI and underimmunized rates (fewer than three doses) are highly heterogeneous across Pakistan (Figs. 1). Both zero dose RI and underimmunization rates were high in most of Punjab, Sindh, and KP provinces, and lowest in the western provinces, Balochistan and FATA.

### Conclusions

The risk of poliovirus has decreased dramatically in many of the key reservoir areas in Pakistan. The results of this model have been used to prioritize sub-national areas in Pakistan to receive additional immunization activities, additional monitoring, or other special interventions.

Steve Kroiss , Mike Famulare , Hil Lyons , Kevin McCarthy , Guillaume Chabot-Couture , Steve J. Kroiss, Michael Famulare, Hil Lyons, Kevin A. McCarthy, Laina D. Mercer, Guillaume Chabot-Couture

Vaccine

The globally synchronized removal of the attenuated Sabin type 2 strain from the oral polio vaccine (OPV) in April 2016 marked a major change in polio vaccination policy. This change will provide a significant reduction in the burden of vaccine-associated paralytic polio (VAPP), but may increase the risk of circulating vaccine-derived poliovirus (cVDPV2) outbreaks during the transition period. This risk can be monitored by tracking the disappearance of Sabin-like type 2 (SL2) using data from the polio surveillance system. We studied SL2 prevalence in 17 countries in Africa and Asia, from 2010 to 2016 using acute flaccid paralysis surveillance data. We modeled the peak and decay of SL2 prevalence following mass vaccination events using a beta-binomial model for the detection rate, and a Ricker function for the temporal dependence. We found type 2 circulated the longest of all serotypes after a vaccination campaign, but that SL2 prevalence returned to baseline levels in approximately 50 days. Post-cessation model predictions identified 19 anomalous SL2 detections outside of model predictions in Afghanistan, India, Nigeria, Pakistan, and western Africa. Our models established benchmarks for the duration of SL2 detection after OPV2 cessation. As predicted, SL2 detection rates have plummeted, except in Nigeria where OPV2 use continued for some time in response to recent cVDPV2 detections. However, the anomalous SL2 detections suggest specific areas that merit enhanced monitoring for signs of cVDPV2 outbreaks.

Kevin McCarthy , Guillaume Chabot-Couture , Mike Famulare , Hil Lyons , Kevin A. McCarthy, Guillaume Chabot-Couture, Michael Famulare, Hil M. Lyons and Laina D. Mercer

BMC Medicine

### Background

Wild type 2 poliovirus was last observed in 1999. The Sabin-strain oral polio vaccine type 2 (OPV2) was critical to eradication, but it is known to revert to a neurovirulent phenotype, causing vaccine-associated paralytic poliomyelitis. OPV2 is also transmissible and can establish circulating lineages, called circulating vaccine-derived polioviruses (cVDPVs), which can also cause paralytic outbreaks. Thus, in April 2016, OPV2 was removed from immunization activities worldwide. Interrupting transmission of cVDPV2 lineages that survive cessation will require OPV2 in outbreak response, which risks seeding new cVDPVs. This potential cascade of outbreak responses seeding VDPVs, necessitating further outbreak responses, presents a critical risk to the OPV2 cessation effort.

### Methods

The EMOD individual-based disease transmission model was used to investigate OPV2 use in outbreak response post-cessation in West African populations. A hypothetical outbreak response in northwest Nigeria is modeled, and a cVDPV2 lineage is considered established if the Sabin strain escapes the response region and continues circulating 9 months post-response. The probability of this event was investigated in a variety of possible scenarios.

### Results

Under a broad range of scenarios, the probability that widespread OPV2 use in outbreak response (~2 million doses) establishes new cVDPV2 lineages in this model may exceed 50% as soon as 18 months or as late as 4 years post-cessation.

### Conclusions

The risk of a cycle in which outbreak responses seed new cVDPV2 lineages suggests that OPV2 use should be managed carefully as time from cessation increases. It is unclear whether this risk can be mitigated in the long term, as mucosal immunity against type 2 poliovirus declines globally. Therefore, current programmatic strategies should aim to minimize the possibility that continued OPV2 use will be necessary in future years: conducting rapid and aggressive outbreak responses where cVDPV2 lineages are discovered, maintaining high-quality surveillance in all high-risk settings, strengthening the use of the inactivated polio vaccine as a booster in the OPV2-exposed and in routine immunization, and gaining access to currently inaccessible areas of the world to conduct surveillance.

Mike Famulare , Dr Mami Taniuchi, PhD, Michael Famulare, PhD, Khalequ Zaman, PhD, Md Jashim Uddin, MSc, Alexander M Upfill-Brown, MSc, Tahmina Ahmed, MSc, Parimalendu Saha, MSc, Rashidul Haque, PhD, Ananda S Bandyopadhyay, MBBS, Prof John F Modlin, MD, James A Platts-Mills, MD, Prof Eric R Houpt, MD, Mohammed Yunus, MBBS, Prof William A Petri Jr, MD

The Lancet Infectious Diseases

### Background

Trivalent oral polio vaccine (tOPV) was replaced worldwide from April, 2016, by bivalent types 1 and 3 oral polio vaccine (bOPV) and one dose of inactivated polio vaccine (IPV) where available. The risk of transmission of type 2 poliovirus or Sabin 2 virus on re-introduction or resurgence of type 2 poliovirus after this switch is not understood completely. We aimed to assess the risk of Sabin 2 transmission after a polio vaccination campaign with a monovalent type 2 oral polio vaccine (mOPV2).

### Methods

We did an open-label cluster-randomised trial in villages in the Matlab region of Bangladesh. We randomly allocated villages (clusters) to either: tOPV at age 6 weeks, 10 weeks, and 14 weeks; or bOPV at age 6 weeks, 10 weeks, and 14 weeks and either one dose of IPV at age 14 weeks or two doses of IPV at age 14 weeks and 18 weeks. After completion of enrolment, we implemented an mOPV2 vaccination campaign that targeted 40% of children younger than 5 years, regardless of enrolment status. The primary outcome was Sabin 2 incidence in the 10 weeks after the campaign in per-protocol infants who did not receive mOPV2, as assessed by faecal shedding of Sabin 2 by reverse transcriptase quantitative PCR (RT-qPCR). The effect of previous immunity on incidence was also investigated with a dynamical model of poliovirus transmission to observe prevalence and incidence of Sabin 2 virus. This trial is registered at ClinicalTrials.gov, number NCT02477046.

### Findings

Between April 30, 2015, and Jan 14, 2016, individuals from 67 villages were enrolled to the study. 22 villages (300 infants) were randomly assigned tOPV, 23 villages (310 infants) were allocated bOPV and one dose of IPV, and 22 villages (329 infants) were assigned bOPV and two doses of IPV. Faecal shedding of Sabin 2 in infants who did not receive the mOPV2 challenge did not differ between children immunised with bOPV and one or two doses of IPV and those who received tOPV (15 of 252 [6%] vs six of 122 [4%]; odds ratio [OR] 1·29, 95% CI 0·45–3·72; p=0·310). However, faecal shedding of Sabin 2 in household contacts was increased significantly with bOPV and one or two doses of IPV compared with tOPV (17 of 751 [2%] vs three of 353 [1%]; OR 3·60, 95% CI 0·82–15·9; p=0·045). Dynamical modelling of within-household incidence showed that immunity in household contacts limited transmission.

### Interpretation

In this study, simulating 1 year of tOPV cessation, Sabin 2 transmission was higher in household contacts of mOPV2 recipients in villages receiving bOPV and either one or two doses of IPV, but transmission was not increased in the community as a whole as shown by the non-significant difference in incidence among infants. Dynamical modelling indicates that transmission risk will be higher with more time since cessation.

### Funding

Bill & Melinda Gates Foundation.

Kevin McCarthy , Guillaume Chabot-Couture , Kevin A. McCarthy, Guillaume Chabot-Couture, and Faisal Shuaib

A spatial model of Wild Poliovirus Type 1 in Kano State, Nigeria

Background
Since the launch of the Global Polio Eradication Initiative, all but three countries (Nigeria, Pakistan, and Afghanistan) have apparently interrupted all wild poliovirus (WPV) transmission, and only one of three wild serotypes has been reported globally since 2012. Countrywide supplemental immunization campaigns in Nigeria produced dramatic reduction in WPV Type 1 paralysis cases since 2010 compared to the 2000’s, and WPV1 has not been observed in Nigeria since July 24, 2014. This article presents the development and calibration of a spatial metapopulation model of wild poliovirus Type 1 transmission in Kano State, Nigeria, which was the location of the most recent WPV1 case and 5 out of 6 of the reported WPV1 paralytic cases in Nigeria in 2014.

Methods
The model is calibrated to data on the case counts and age at onset of paralysis from 2003–2009. The features of the data drive model development from a simple susceptible-exposed-infective-recovered (SEIR) model to a spatial metapopulation model featuring seasonal forcing and age-dependent transmission. The calibrated parameter space is then resampled, projected forward, and compared to more recent case counts to estimate the probability that Type 1 poliovirus has been eliminated in Kano state.

Results
The model indicates a 91 % probability that Type 1 poliovirus has been eliminated from Kano state as of October 2015. This probability rises to >99 % if no WPV1 paralysis cases are detected for another year. The other states in Nigeria have experienced even longer case-free periods (the only other state with a WPV1 case was Yobe, on April 19, 2014), and Nigeria is the last remaining country in Africa to experience endemic WPV1 transmission, so these results can be interpreted as an upper bound on the probability that WPV1 transmission is currently interrupted continent-wide.

Conclusions
While the results indicate optimism that WPV1 transmission has been interrupted in Kano state, the model also assumes that frequent SIAs with high coverage continue to take place in Kano state through the end of the certification period. We conclude that though WPV1 appears to be on the brink of continent-wide elimination (WHO officially removed Nigeria from the list of polio-endemic countries on September 25, 2015), it is important for the polio program to maintain vigilance in surveillance and vaccination activities to prevent WPV1 resurgence through the WHO’s 3-year eradication certification period.

Guillaume Chabot-Couture , Hil Lyons , Alexander M. Upfill-Brown, Arend Voorman, Guillaume Chabot-Couture, Faisal Shuaib, Hil M. Lyons

BMC Medicine

Background The world is closer than ever to a polio-free Africa. In this end-stage, it is important to ensure high levels of population immunity to prevent polio outbreaks. Here, we introduce a new method of assessing vaccination campaign effectiveness and estimating immunity at the district-level. We demonstrate how this approach can be used to plan the vaccination campaigns prospectively to better manage population immunity in Northern Nigeria.

Methods Using Nigerian acute flaccid paralysis surveillance data from 2004–2014, we developed a Bayesian hierarchical model of campaign effectiveness and compared it to lot-quality assurance sampling data. We then used reconstructed sero-specific population immunity based on campaign history and compared district estimates of immunity to the occurrence of confirmed poliovirus cases.

Results Estimated campaign effectiveness has improved across northern Nigeria since 2004, with Kano state experiencing an increase of 40 % (95 % CI, 26–54 %) in effectiveness from 2013 to 2014. Immunity to type 1 poliovirus has increased steadily. On the other hand, type 2 immunity was low and variable until the recent use of trivalent oral polio vaccine. We find that immunity estimates are related to the occurrence of both wild and vaccine-derived poliovirus cases and that campaign effectiveness correlates with direct measurements using lot-quality assurance sampling. Future campaign schedules highlight the trade-offs involved with using different vaccine types.

Conclusions The model in this study provides a novel method for assessing vaccination campaign performance and epidemiologically-relevant estimates of population immunity. Small-area estimates of campaign effectiveness can then be used to evaluate prospective campaign plans. This modeling approach could be applied to other countries as well as other vaccine preventable diseases.

Guillaume Chabot-Couture , Alexandra E. Brown, Hiromasa Okayasu, Michael M. Nzioki, Mufti Z. Wadood, Guillaume Chabot-Couture, Arshad Quddus, George Walker and Roland W. Sutter

The Journal of Infectious Diseases

Monitoring the quality of supplementary immunization activities (SIAs) is a key tool for polio eradication. Regular monitoring data, however, are often unreliable, showing high coverage levels in virtually all areas, including those with ongoing virus circulation. To address this challenge, lot quality assurance sampling (LQAS) was introduced in 2009 as an additional tool to monitor SIA quality. Now used in 8 countries, LQAS provides a number of programmatic benefits: identifying areas of weak coverage quality with statistical reliability, differentiating areas of varying coverage with greater precision, and allowing for trend analysis of campaign quality. LQAS also accommodates changes to survey format, interpretation thresholds, evaluations of sample size, and data collection through mobile phones to improve timeliness of reporting and allow for visualization of campaign quality. LQAS becomes increasingly important to address remaining gaps in SIA quality and help focus resources on high-risk areas to prevent the continued transmission of wild poliovirus.

Mike Famulare , Stewart Chang , Michael Famulare, Stewart Chang, Jane Iber, Kun Zhao, Johnson A. Adeniji, David Bukbuk, Marycelin Baba, Matthew Behrend, Cara C. Burns and M. Steven Oberste

Journal of Virology

To assess the dynamics of genetic reversion of live poliovirus vaccine in humans, we studied molecular evolution in Sabin-like poliovirus isolates from Nigerian acute flaccid paralysis cases obtained from routine surveillance. We employed a novel modeling approach to infer substitution and recombination rates from whole-genome sequences and information about poliovirus infection dynamics and individual vaccination history. We confirmed observations from a recent vaccine trial that VP1 substitution rates are increased for Sabin-like isolates relative to the wild-type rate due to increased non-synonymous substitution rates. We also inferred substitution rates for attenuating nucleotides and confirmed that reversion can occur in days to weeks after vaccination. We combine our observations for Sabin-like evolution with the wild-type circulating VP1 molecular clock to infer that the mean time from the initiating vaccine dose to the earliest detection of circulating vaccine-derived poliovirus (cVDPV) is 300 days for type 1, 210 days for type 2, and 390 days for type 3. Phylogenetic relationships indicated transient local transmission of Sabin 3 and possibly Sabin 1 during periods of low wild polio incidence. Comparison of Sabin-like recombinants with known Nigerian VDPV recombinants shows that while recombination with non-Sabin enteroviruses is associated with cVDPV, the recombination rates are similar for Sabin-Sabin and Sabin-non-Sabin enterovirus recombination after accounting for time from dose to detection. Our study provides a comprehensive picture of the evolutionary dynamics of oral polio vaccine in the field.

IMPORTANCE The global polio eradication effort has completed its twenty-sixth year. Despite success in eliminating wild poliovirus from most of the world, polio persists in populations where logistical, social, and political factors have not allowed for vaccination programs of sustained high quality. One issue of critical importance is eliminating circulating vaccine-derived poliovirus (cVDPV) that have properties indistinguishable from wild poliovirus and can cause paralytic disease. cVDPV emerges due to the genetic instability of the Sabin viruses used in oral polio vaccine (OPV) in populations that have low immunity to poliovirus. However, the dynamics responsible are incompletely understood because it has historically been difficult to gather and interpret data about OPV evolution in regions where cVDPV has occurred. This study is the first to combine whole-genome sequencing of poliovirus isolates collected during routine surveillance with knowledge about polio intra-host dynamics to provide quantitative insight into polio vaccine evolution in the field.

Mike Famulare , Michael Famulare

PLoS ONE

Wild poliovirus type 3 (WPV3) has not been seen anywhere since the last case of WPV3-associated paralysis in Nigeria in November 2012. At the time of writing, the most recent case of wild poliovirus type 1 (WPV1) in Nigeria occurred in July 2014, and WPV1 has not been seen in Africa since a case in Somalia in August 2014. No cases associated with circulating vaccine-derived type 2 poliovirus (cVDPV2) have been detected in Nigeria since November 2014. Has WPV1 been eliminated from Africa? Has WPV3 been eradicated globally? Has Nigeria interrupted cVDPV2 transmission? These questions are difficult because polio surveillance is based on paralysis and paralysis only occurs in a small fraction of infections. This report provides estimates for the probabilities of poliovirus elimination in Nigeria given available data as of March 31, 2015. It is based on a model of disease transmission that is built from historical polio incidence rates and is designed to represent the uncertainties in transmission dynamics and poliovirus detection that are fundamental to interpreting long time periods without cases. The model estimates that, as of March 31, 2015, the probability of WPV1 elimination in Nigeria is 84%, and that if WPV1 has not been eliminated, a new case will be detected with 99% probability by the end of 2015. The probability of WPV3 elimination (and thus global eradication) is > 99%. However, it is unlikely that the ongoing transmission of cVDPV2 has been interrupted; the probability of cVDPV2 elimination rises to 83% if no new cases are detected by April 2016.

Bradley Wagner , Daniel Klein , Bradley Wagner, Matthew Behrend, Daniel Klein, Alexander Upfill-Brown, Philip Eckhoff, and Hao Hu

PLoS ONE

A priority of the Global Polio Eradication Initiative (GPEI) 2013–2018 strategic plan is to evaluate the potential impact on polio eradication resulting from expanding one or more Supplementary Immunization Activities (SIAs) to children beyond age five-years in polio endemic countries. It has been hypothesized that such expanded age group (EAG) campaigns could accelerate polio eradication by eliminating immunity gaps in older children that may have resulted from past periods of low vaccination coverage. Using an individual-based mathematical model, we quantified the impact of EAG campaigns in terms of probability of elimination, reduction in polio transmission and age stratified immunity levels. The model was specifically calibrated to seroprevalence data from a polio-endemic region: Zaria, Nigeria. We compared the impact of EAG campaigns, which depend only on age, to more targeted interventions which focus on reaching missed populations. We found that EAG campaigns would not significantly improve prospects for polio eradication; the probability of elimination increased by 8% (from 24% at baseline to 32%) when expanding three annual SIAs to 5–14 year old children and by 18% when expanding all six annual SIAs. In contrast, expanding only two of the annual SIAs to target hard-to-reach populations at modest vaccination coverage—representing less than one tenth of additional vaccinations required for the six SIA EAG scenario—increased the probability of elimination by 55%. Implementation of EAG campaigns in polio endemic regions would not improve prospects for eradication. In endemic areas, vaccination campaigns which do not target missed populations will not benefit polio eradication efforts.

Hil Lyons , Guillaume Chabot-Couture , Alexander Upfill-Brown, Hil Lyons, Muhammad A Pate, Faisal Shuaib, Shahzad Baig, Hao Hu, Philip Eckhoff, and Guillaume Chabot-Couture

BMC Medicine

Background
One of the challenges facing the Global Polio Eradication Initiative is efficiently directing limited resources, such as specially trained personnel, community outreach activities, and satellite vaccinator tracking, to the most at-risk areas to maximize the impact of interventions. A validated predictive model of wild poliovirus circulation would greatly inform prioritization efforts by accurately forecasting areas at greatest risk, thus enabling the greatest effect of program interventions.

Methods
Using Nigerian acute flaccid paralysis surveillance data from 2004-2013, we developed a spatial hierarchical Poisson hurdle model fitted within a Bayesian framework to study historical polio caseload patterns and forecast future circulation of type 1 and 3 wild poliovirus within districts in Nigeria. A Bayesian temporal smoothing model was applied to address data sparsity underlying estimates of covariates at the district level.

Results
We find that calculated vaccine-derived population immunity is significantly negatively associated with the probability and number of wild poliovirus case(s) within a district. Recent case information is significantly positively associated with probability of a case, but not the number of cases. We used lagged indicators and coefficients from the fitted models to forecast reported cases in the subsequent six-month periods. Over the past three years, the average predictive ability is 86 ± 2% and 85 ± 4% for wild poliovirus type 1 and 3, respectively. Interestingly, the predictive accuracy of historical transmission patterns alone is equivalent (86 ± 2% and 84 ± 4% for type 1 and 3, respectively). We calculate uncertainty in risk ranking to inform assessments of changes in rank between time periods.

Conclusions
The model developed in this study successfully predicts districts at risk for future wild poliovirus cases in Nigeria. The highest predicted district risk was 12.8 WPV1 cases in 2006, while the lowest district risk was 0.001 WPV1 cases in 2013. Model results have been used to direct the allocation of many different interventions, including political and religious advocacy visits. This modeling approach could be applied to other vaccine preventable diseases for use in other control and elimination programs.

Matthew R. Behrend, Hao Hu, Karima R. Nigmatulina, and Philip Eckhoff

International Journal of Infectious Diseases

Objective
To examine forces that drive vaccination policy to eradicate wild- and vaccine-derived poliovirus, and to focus on the efficacy of vaccines to support decision-making and further research.

Methods
We searched PubMed and Ovid databases for English-language publications, without date restrictions. We also collected references from major reviews on polio vaccine immunogenicity or protection. We conducted a meta-analysis of human immunity to polio infections using multiple non-linear regression, and built a database from a broad (but not systematic) set of polio vaccine studies (46 studies, >10 000 subjects).

Results
The outcome was an immunological model representative of many different datasets. Parameters measured immunogenicity to both humoral and mucosal immune compartments for Salk and Sabin vaccines. The immunity model was more highly correlated with the data than a simpler per-dose efficacy model.

Conclusions
The model offers new insights for immunization policy. We measured the mucosal immunogenicity of IPV to a precision that is useful in decision-making for end-game polio immunization policies.

The respiratory disease research program at IDM provides analytic support to research, policy, and implementation partners on a range of diseases, including pneumonia, RSV, and influenza.

Our pneumonia research centers on questions of local-elimination feasibility, critical community size for endemic transmission, and the role of herd protection from vaccination. To support these efforts, we use detailed mathematical models of pneumococcal colonization and transmission, which are calibrated to historical studies and recent trials that inform our understanding of family structure and strain-specific immunity.

More broadly, our research on respiratory pathogens, a leading cause of childhood mortality, has explored patterns of seasonality, severity, and co-infection for a variety of viral pathogens observed in hospital cases. That work has been extended to explore the expected impact of maternal and childhood vaccination strategies for RSV and to relate the predictive power of online search trends to regional epidemic characteristics.

Our influenza research targets improved pandemic preparedness through a more detailed understanding of the regional transmission characteristics of seasonal flu -- importation, spatial connectivity, and contact patterns (household, workplace, schools). Through our involvement in the Seattle Flu Study -- including geo-statistical modeling and phylogenetic inference -- our goal is to advance the real-time awareness of disease dynamics and to demonstrate the potential of novel diagnostic and intervention strategies.

Some areas of work include:

• Seasonality of Respiratory Viruses Causing Hospitalizations for ARI (Vietnam).
• Identifying Transmission Routes of S.pneumoniae.

Navideh Noori , Mollie Van Gordon , Brittany Hagedorn , Ben Althouse , Edward Wenger , Andre Lin Ouedraogo , Laura Skrip, Karim Derra, Mikaila Kaboré, Navideh Noori, Adama Gansané, Innocent Valéa, Halidou Tinto, Bicaba W. Brice, Mollie Van Gordon, Brittany Hagedorn, Hervé Hien, Benjamin M. Althouse, Edward A. Wenger, André Lin Ouédraogo

International Journal of Infectious Diseases

### Background

Absolute numbers of COVID-19 cases and deaths reported to date in the sub-Saharan Africa (SSA) region have been significantly lower than those across the Americas, Asia, and Europe. As a result, there has been limited information about the demographic and clinical characteristics of deceased cases in the region, as well as the impacts of different case management strategies.

### Methods

Data from deceased cases reported across SSA through May 10, 2020 and from hospitalized cases in Burkina Faso through April 15, 2020 were analyzed. Demographic, epidemiological, and clinical information on deceased cases in SSA was derived through a line-list of publicly available information and, for cases in Burkina Faso, from aggregate records at the Centre Hospitalier Universitaire de Tengandogo in Ouagadougou. A synthetic case population was derived probabilistically using distributions of age, sex, and underlying conditions from populations of West African countries to assess individual risk factors and treatment effect sizes. Logistic regression analysis was conducted to evaluate the adjusted odds of survival for patients receiving oxygen therapy or convalescent plasma, based on therapeutic effectiveness observed for other respiratory illnesses.

### Results

Across SSA, deceased cases for which demographic data are available have been predominantly male (63/103, 61.2%) and over 50 years of age (59/75, 78.7%). In Burkina Faso, specifically, the majority of deceased cases either did not seek care at all or were hospitalized for a single day (59.4%, 19/32); hypertension and diabetes were often reported as underlying conditions. After adjustment for sex, age, and underlying conditions in the synthetic case population, the odds of mortality for cases not receiving oxygen therapy was significantly higher than those receiving oxygen, such as due to disruptions to standard care (OR: 2.07; 95% CI: 1.56 – 2.75). Cases receiving convalescent plasma had 50% reduced odds of mortality than those who did not (95% CI: 0.24 – 0.93).

### Conclusions

Investment in sustainable production and maintenance of supplies for oxygen therapy, along with messaging around early and appropriate use for healthcare providers, caregivers, and patients could reduce COVID-19 deaths in SSA. Further investigation into convalescent plasma is warranted, as data on its effectiveness specifically in treating COVID-19 becomes available. The success of supportive or curative clinical interventions will depend on earlier treatment seeking, such that community engagement and risk communication will be critical components of the response.

Ben Althouse , Bradley Wagner , B. M. ALTHOUSE, L. L. HAMMITT, L. GRANT, B. G. WAGNER, R. REID, F. LARZELERE-HINTON, R. WEATHERHOLTZ, K. P. KLUGMAN, G. L. RODGERS, K. L. O'BRIEN and H. HU

Epidemiology and Infection

Identifying the transmission sources and reservoirs of Streptococcus pneumoniae (SP) is a long-standing question for pneumococcal epidemiology, transmission dynamics, and vaccine policy. Here we use serotype to identify SP transmission and examine acquisitions (in the same household, local community, and county, or of unidentified origin) in a longitudinal cohort of children and adults from the Navajo Nation and the White Mountain Apache American Indian Tribes. We found that adults acquire SP relatively more in the household than other age groups, and children 2–8 years old typically acquire in their own or surrounding communities. Age-specific transmission probability matrices show that transmissions within household were mostly seen from older to younger siblings. Outside the household, children most often transmit to other children in the same age group, showing age-assortative mixing behavior. We find toddlers and older children to be most involved in SP transmission and acquisition, indicating their role as key drivers of SP epidemiology. Although infants have high carriage prevalence, they do not play a central role in transmission of SP compared with toddlers and older children. Our results are relevant to inform alternative pneumococcal conjugate vaccine dosing strategies and analytic efforts to inform optimization of vaccine programs, as well as assessing the transmission dynamics of pathogens transmitted by close contact in general.

Ben Althouse , Haedi DeAngelis, Samuel V. Scarpino, Meagan C. Fitzpatrick, Alison P. Galvani, Benjamin M. Althouse

JAMA Pediatrics

Importance Current acellular pertussis vaccines may not protect against transmission of Bordetella pertussis.

Objective To assess whether a priming dose of whole-cell pertussis (wP) vaccine is cost-effective at reducing pertussis infection in infants.

Design, Setting, and Participants Mathematical model of pertussis transmission fit to US incidence data in a simulation of the US population. In this simulation study conducted from June 2014 to May 2015, the population was divided into 9 age groups corresponding to the current pertussis vaccination schedule and fit to 2012 pertussis incidence.

Interventions Inclusion of a priming dose of wP vaccine into the current acellular pertussis vaccination schedule.

Main Outcomes and Measures Reductions in symptomatic pertussis incidence by age group, increases in wP vaccine–related adverse effects, and quality-adjusted life-years owing to changing vaccine schedule.

Results Switching to a wP-priming vaccination strategy could reduce whooping cough incidence by up to 95% (95% CI, 91-98), including 96% (95% CI, 92-98) fewer infections in neonates. Although there may be an increase in the number of vaccine adverse effects, we nonetheless estimate a 95% reduction in quality-adjusted life-years lost with a switch to the combined strategy and a cost reduction of 94% (95% CI, 91-97), saving more than \$142 million annually.

Conclusions and Relevance Our results suggest that an alternative vaccination schedule including 1 dose of wP vaccine may be highly cost-effective and ethically preferred until next-generation pertussis vaccines become available.

Ben Althouse , Benjamin M. Althouse and Samuel V. Scarpino

BMC Medicine

### Background

The recent increase in whooping cough incidence (primarily caused by Bordetella pertussis) presents a challenge to both public health practitioners and scientists trying to understand the mechanisms behind its resurgence. Three main hypotheses have been proposed to explain the resurgence: 1) waning of protective immunity from vaccination or natural infection over time, 2) evolution of B. pertussis to escape protective immunity, and 3) low vaccine coverage. Recent studies have suggested a fourth mechanism: asymptomatic transmission from individuals vaccinated with the currently used acellular B. pertussis vaccines.

### Methods

Using wavelet analyses of B. pertussis incidence in the United States (US) and United Kingdom (UK) and a phylodynamic analysis of 36 clinical B. pertussis isolates from the US, we find evidence in support of asymptomatic transmission of B. pertussis. Next, we examine the clinical, public health, and epidemiological consequences of asymptomatic B. pertussis transmission using a mathematical model.

### Results

We find that: 1) the timing of changes in age-specific attack rates observed in the US and UK are consistent with asymptomatic transmission; 2) the phylodynamic analysis of the US sequences indicates more genetic diversity in the overall bacterial population than would be suggested by the observed number of infections, a pattern expected with asymptomatic transmission; 3) asymptomatic infections can bias assessments of vaccine efficacy based on observations of B. pertussis-free weeks; 4) asymptomatic transmission can account for the observed increase in B. pertussis incidence; and 5) vaccinating individuals in close contact with infants too young to receive the vaccine (“cocooning” unvaccinated children) may be ineffective.

### Conclusions

Although a clear role for the previously suggested mechanisms still exists, asymptomatic transmission is the most parsimonious explanation for many of the observations surrounding the resurgence of B. pertussis in the US and UK. These results have important implications for B. pertussis vaccination policy and present a complicated scenario for achieving herd immunity and B. pertussis eradication.

The TB research program at IDM provides analytical support to our research, policy, and implementation partners. These include analyses to identify priority areas for research, as well as impact estimation for interventions that can be used to develop strategic plans, target product profiles, and field studies. To support these efforts, we have developed a very flexible individual-based modeling software tool, EMOD-TB-HIV (which uses overlapping components with EMOD-HIV in order to capture the effects of co-infection and HIV treatment on TB progression), for which source code and documentation are freely available online, and training is available on request both through IDM and our research collaborator network.

Current priorities for our research agenda include:

• Use cases for emerging TB diagnostics, interventions to reduce vulnerability to TB (such as nutrition and smoking cessation.
• The role of social network structures in determining which interventions work best to accelerate reductions in TB incidence and burden.

Bradley Wagner , Michelle A Bulterys, Bradley Wagner, Mael Redard-Jacot, Anita Suresh, Nira R. Pollock, Emmanuel Moreau, Claudia M. Denkinger, Paul K. Drain, Tobias Broger

Journal of Clinical Medicine

Most diagnostic tests for tuberculosis (TB) rely on sputum samples, which are difficult to obtain and have low sensitivity in immunocompromised patients, patients with disseminated TB, and children, delaying treatment initiation. The World Health Organization (WHO) calls for the development of a rapid, biomarker-based, non-sputum test capable of detecting all forms of TB at the point-of-care to enable immediate treatment initiation. Lipoarabinomannan (LAM) is the only WHO-endorsed TB biomarker that can be detected in urine, an easily collected sample. This status update discusses the characteristics of LAM as a biomarker, describes the performance of first-generation urine LAM tests and reasons for slow uptake, and presents considerations for developing the next generation of more sensitive and impactful tests. Next-generation urine LAM tests have the potential to reach adult and pediatric patients regardless of HIV status or site of infection and facilitate global TB control. Implementation and scale-up of existing LAM tests and development of next-generation assays should be prioritized.

Stewart Chang , Bradley Wagner , Stewart T. Chang, Violet N. Chihota, Katherine L. Fielding, Alison D. Grant, Rein M. Houben, Richard G. White, Gavin J. Churchyard, Philip A. Eckhoff, and Bradley G. Wagner

BMC Medicine

### Background

Gold mines represent a potential hotspot for Mycobacterium tuberculosis (Mtb) transmission and may be exacerbating the tuberculosis (TB) epidemic in South Africa. However, the presence of multiple factors complicates estimation of the mining contribution to the TB burden in South Africa.

### Methods

We developed two models of TB in South Africa, a static risk model and an individual-based model that accounts for longer-term trends. Both models account for four populations — mine workers, peri-mining residents, labor-sending residents, and other residents of South Africa — including the size and prevalence of latent TB infection, active TB, and HIV of each population and mixing between populations. We calibrated to mine- and country-level data and used the static model to estimate force of infection (FOI) and new infections attributable to local residents in each community compared to other residents. Using the individual-based model, we simulated a counterfactual scenario to estimate the fraction of overall TB incidence in South Africa attributable to recent transmission in mines.

### Results

We estimated that the majority of FOI in each community is attributable to local residents: 93.9% (95% confidence interval 92.4–95.1%), 91.5% (91.4–91.5%), and 94.7% (94.7–94.7%) in gold mining, peri-mining, and labor-sending communities, respectively. Assuming a higher rate of Mtb transmission in mines, 4.1% (2.6–5.8%), 5.0% (4.5–5.5%), and 9.0% (8.8–9.1%) of new infections in South Africa are attributable to gold mine workers, peri-mining residents, and labor-sending residents, respectively. Therefore, mine workers with TB disease, who constitute ~ 2.5% of the prevalent TB cases in South Africa, contribute 1.62 (1.04–2.30) times as many new infections as TB cases in South Africa on average. By modeling TB on a longer time scale, we estimate 63.0% (58.5–67.7%) of incident TB disease in gold mining communities to be attributable to recent transmission, of which 92.5% (92.1–92.9%) is attributable to local transmission.

### Conclusions

Gold mine workers are estimated to contribute a disproportionately large number of Mtb infections in South Africa on a per-capita basis. However, mine workers contribute only a small fraction of overall Mtb infections in South Africa. Our results suggest that curtailing transmission in mines may have limited impact at the country level, despite potentially significant impact at the mining level.

Stewart Chang , Bradley Wagner , Prof Nicolas A Menzies, PhD, Gabriela B Gomez, PhD, Fiammetta Bozzani, MSc, Susmita Chatterjee, PhD, Nicola Foster, MPH, Ines Garcia Baena, MSc, Yoko V Laurence, MSc, Prof Sun Qiang, PhD, Andrew Siroka, PhD, Sedona Sweeney, MSc, Stéphane Verguet, PhD, Nimalan Arinaminpathy, DPhil, Andrew S Azman, PhD, Eran Bendavid, MD, Stewart T Chang, PhD, Prof Ted Cohen, DPH, Justin T Denholm, PhD, David W Dowdy, MD, Philip A Eckhoff, PhD, Jeremy D Goldhaber-Fiebert, PhD, Andreas Handel, PhD, Grace H Huynh, PhD, Marek Lalli, MSc, Hsien-Ho Lin, ScD, Sandip Mandal, PhD, Emma S McBryde, PhD, Surabhi Pandey, PhD, Prof Joshua A Salomon, PhD, Sze-chuan Suen, MS, Tom Sumner, PhD, James M Trauer, MBBS, Bradley G Wagner, PhD, Prof Christopher C Whalen, MD, Chieh-Yin Wu, MS, Delia Boccia, PhD, Vineet K Chadha, MD, Salome Charalambous, PhD, Daniel P Chin, MD, Prof Gavin Churchyard, PhD, Colleen Daniels, MA, Puneet Dewan, MD, Lucica Ditiu, MD, Jeffrey W Eaton, PhD, Prof Alison D Grant, PhD, Piotr Hippner, MSc, Mehran Hosseini, MD, David Mametja, MPH, Carel Pretorius, PhD, Yogan Pillay, PhD, Kiran Rade, MD, Suvanand Sahu, MD, Lixia Wang, MS, Rein M G J Houben, PhD, Michael E Kimerling, MD, Richard G White, PhD, Anna Vassall, PhD

The Lancet

Background
The post-2015 End TB Strategy sets global targets of reducing tuberculosis incidence by 50% and mortality by 75% by 2025. We aimed to assess resource requirements and cost-effectiveness of strategies to achieve these targets in China, India, and South Africa.

Methods
We examined intervention scenarios developed in consultation with country stakeholders, which scaled up existing interventions to high but feasible coverage by 2025. Nine independent modelling groups collaborated to estimate policy outcomes, and we estimated the cost of each scenario by synthesising service use estimates, empirical cost data, and expert opinion on implementation strategies. We estimated health effects (ie, disability-adjusted life-years averted) and resource implications for 2016–35, including patient-incurred costs. To assess resource requirements and cost-effectiveness, we compared scenarios with a base case representing continued current practice.

Findings
Incremental tuberculosis service costs differed by scenario and country, and in some cases they more than doubled existing funding needs. In general, expansion of tuberculosis services substantially reduced patient-incurred costs and, in India and China, produced net cost savings for most interventions under a societal perspective. In all three countries, expansion of access to care produced substantial health gains. Compared with current practice and conventional cost-effectiveness thresholds, most intervention approaches seemed highly cost-effective.

Interpretation
Expansion of tuberculosis services seems cost-effective for high-burden countries and could generate substantial health and economic benefits for patients, although substantial new funding would be required. Further work to determine the optimal intervention mix for each country is necessary.

Figure 2 Incremental patient-incurred costs for 2016–35, for each intervention scenario, compared with the base case, by country and model.

Funding

Bill and Melinda Gates Foundation

Stewart Chang , Bradley Wagner , Dr Rein M G J Houben, PhD, Nicolas A Menzies, PhD, Tom Sumner, PhD, Grace H Huynh, PhD, Nimalan Arinaminpathy, PhD, Jeremy D Goldhaber-Fiebert, PhD, Hsien-Ho Lin, PhD, Chieh-Yin Wu, MS, Sandip Mandal, PhD, Surabhi Pandey, PhD, Sze-chuan Suen, MS, Eran Bendavid, MD, Andrew S Azman, PhD, David W Dowdy, PhD, Nicolas Bacaër, PhD, Allison S Rhines, PhD, Prof Marcus W Feldman, PhD, Andreas Handel, PhD, Prof Christopher C Whalen, MD, Stewart T Chang, PhD, Bradley G Wagner, PhD, Philip A Eckhoff, PhD, James M Trauer, PhD, Justin T Denholm, PhD, Prof Emma S McBryde, PhD, Ted Cohen, DPH, Prof Joshua A Salomon, PhD, Carel Pretorius, PhD, Marek Lalli, MSc, Jeffrey W Eaton, PhD, Delia Boccia, PhD, Mehran Hosseini, MD, Gabriela B Gomez, PhD, Suvanand Sahu, MD, Colleen Daniels, MA, Lucica Ditiu, MD, Daniel P Chin, MD, Lixia Wang, MS, Vineet K Chadha, MD, Kiran Rade, MPhil, Puneet Dewan, MD, Piotr Hippner, MSc, Salome Charalambous, PhD, Prof Alison D Grant, Prof Gavin Churchyard, PhD, Yogan Pillay, PhD, L David Mametja, MPH, Michael E Kimerling, MD, Anna Vassall, PhD, Richard G White, PhD

The Lancet

Background
The post-2015 End TB Strategy proposes targets of 50% reduction in tuberculosis incidence and 75% reduction in mortality from tuberculosis by 2025. We aimed to assess whether these targets are feasible in three high-burden countries with contrasting epidemiology and previous programmatic achievements.

Methods
11 independently developed mathematical models of tuberculosis transmission projected the epidemiological impact of currently available tuberculosis interventions for prevention, diagnosis, and treatment in China, India, and South Africa. Models were calibrated with data on tuberculosis incidence and mortality in 2012. Representatives from national tuberculosis programmes and the advocacy community provided distinct country-specific intervention scenarios, which included screening for symptoms, active case finding, and preventive therapy.

Findings
Aggressive scale-up of any single intervention scenario could not achieve the post-2015 End TB Strategy targets in any country. However, the models projected that, in the South Africa national tuberculosis programme scenario, a combination of continuous isoniazid preventive therapy for individuals on antiretroviral therapy, expanded facility-based screening for symptoms of tuberculosis at health centres, and improved tuberculosis care could achieve a 55% reduction in incidence (range 31–62%) and a 72% reduction in mortality (range 64–82%) compared with 2015 levels. For India, and particularly for China, full scale-up of all interventions in tuberculosis-programme performance fell short of the 2025 targets, despite preventing a cumulative 3·4 million cases. The advocacy scenarios illustrated the high impact of detecting and treating latent tuberculosis.

Interpretation
Major reductions in tuberculosis burden seem possible with current interventions. However, additional interventions, adapted to country-specific tuberculosis epidemiology and health systems, are needed to reach the post-2015 End TB Strategy targets at country level.

Daniel Klein , Bradley Wagner , Grace H Huynh, Daniel Klein, Daniel P Chin, Bradley G Wagner, Philip A Eckhoff, Renzhong Liu, and Lixia Wang

BMC Medicine

Background: Significant progress in tuberculosis (TB) control has been achieved worldwide over the last two decades. Global TB mortality has fallen by 45%, and TB incidence is declining. Recently, the World Health Organization (WHO) established an ambitious post-2015 global strategy, the End TB Strategy. This strategy outlines a 2025 milestone of 50% reduction in incidence and 75% reduction in mortality, and an overall 2035 target of 90% reduction in incidence and 95% reduction in mortality. In order to reach these targets, countries will likely need to redouble their TB control efforts and perhaps adopt new TB control strategies.

Between 1992 and 2012, China made impressive progress in TB control. Prior to 1992, most TB patients were treated in private hospitals, where patients typically received low-quality care - improper treatment was widespread, and only approximately 20% of patients had supervised TB treatment. In addition, nearly 50% experienced interrupted or shortened treatment and there was little follow-up of patients who dropped out or relapsed after a treatment episode. Starting in 1992, China ramped up a high-quality directly observed treatment, short-course (DOTS)-based strategy in Center for Disease Control (CDC) public health clinics in 13 provinces covering half the population, requiring hospitals to refer suspected TB patients to the CDC system. In the early 2000s, the DOTS program was expanded nationwide and an Internet-based disease reporting system was introduced [8]-[11], further increasing referrals from the hospital to the CDC system. By 2010 it was estimated that approximately 80% of all TB patients were confirmed and treated within the CDC system [8],[9], where the treatment success rate was estimated to be 85%.

Methods: The present study utilizes the Disease Transmission Kernel (DTK) model developed by the Institute for Disease Modeling group at Intellectual Ventures. The model and all necessary input files are available by request at the Institute for Disease Modeling website. Additional file 1 details the model structure, assumptions, and a complete list of model inputs.

Conclusions: The combination of an aging demographic in China and the increasing role of reactivation disease represents a growing challenge to TB control as China considers its post-2015 strategy. We have constructed a mathematical model of TB transmission at the country level in China, taking into account aging of the population and estimating the contribution of reactivation to overall incidence. The nationwide roll-out of the DOTS program reduced the annual risk of infection(ARI) [81],[82] by improving treatment outcomes and reducing infectiousness from treatment experienced individuals. Given the high population coverage of DOTS in the CDC public health clinics, we estimate that new transmission is not the major driver of overall TB incidence. Rather, reactivation disease, combined with the growing elderly population, will be the major determinant of the decline in TB incidence and mortality over the next two decades.

Daniel Klein , Bradley Wagner , Grace H Huynh, Daniel Klein, Daniel P Chin, Bradley G Wagner, Philip A Eckhoff, Renzhong Liu, and Lixia Wang

BMC Medicine

### Background

In the last 20 years, China ramped up a DOTS (directly observed treatment, short-course)-based tuberculosis (TB) control program with 80% population coverage, achieving the 2015 Millennium Development Goal of a 50% reduction in TB prevalence and mortality. Recently, the World Health Organization developed the End TB Strategy, with an overall goal of a 90% reduction in TB incidence and a 95% reduction in TB deaths from 2015–2035. As the TB burden shifts to older individuals and China’s overall population ages, it is unclear if maintaining the current DOTS strategy will be sufficient for China to reach the global targets.

### Methods

We developed an individual-based computational model of TB transmission, implementing realistic age demographics and fitting to country-level data of age-dependent prevalence over time. We explored the trajectory of TB burden if the DOTS strategy is maintained or if new interventions are introduced using currently available and soon-to-be-available tools. These interventions include increasing population coverage of DOTS, reducing time to treatment, increasing treatment success, and active case finding among elders > 65 years old. We also considered preventative therapy in latently infected elders, a strategy limited by resource constraints and the risk of adverse events.

### Results

Maintenance of the DOTS strategy reduces TB incidence and mortality by 42% (95% credible interval, 27-59%) and 41% (5-64%), respectively, between 2015 and 2035. A combination of all feasible interventions nears the 2035 mortality target, reducing TB incidence and mortality by 59% (50-76%) and 83% (73-94%). Addition of preventative therapy for elders would enable China to nearly reach both the incidence and mortality targets, reducing incidence and mortality by 84% (78-93%) and 92% (86-98%).

### Conclusions

The current decline in incidence is driven by two factors: maintaining a low level of new infections in young individuals and the aging out of older latently infected individuals who contribute incidence due to reactivation disease. While further reducing the level of new infections has a modest effect on burden, interventions that limit reactivation have a greater impact on TB burden. Tools that make preventative therapy more feasible on a large scale and in elders will help China achieve the global targets.