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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.

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


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.


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.


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.



Malaria transmission is both seasonal and heterogeneous, and mathematical models that seek to predict the effects of possible intervention strategies should accurately capture realistic seasonality of vector abundance, seasonal dynamics of within-host effects, and heterogeneity of exposure, which may also vary seasonally.


Prevalence, incidence, asexual parasite and gametocyte densities, and infectiousness measurements from eight study sites in sub-Saharan Africa were used to calibrate an individual-based model with innate and adaptive immunity. Data from the Garki Project was used to fit exposure rates and parasite densities with month-resolution. A model capturing Garki seasonality and seasonal heterogeneity of exposure was used as a framework for characterizing the infectious reservoir of malaria, testing optimal timing of indoor residual spraying, and comparing four possible mass drug campaign implementations for malaria control.


Seasonality as observed in Garki sites is neither sinusoidal nor box-like, and substantial heterogeneity in exposure arises from dry-season biting. Individuals with dry-season exposure likely account for the bulk of the infectious reservoir during the dry season even when they are a minority in the overall population. Spray campaigns offer the most benefit in prevalence reduction when implemented just prior to peak vector abundance, which may occur as late as a couple months into the wet season, and targeting spraying to homes of individuals with dry-season exposure can be particularly effective. Expanding seasonal malaria chemoprevention programs to cover older children is predicted to increase the number of cases averted per treatment and is therefore recommended for settings of seasonal and intense transmission.


Accounting for heterogeneity and seasonality in malaria transmission is critical for understanding transmission dynamics and predicting optimal timing and targeting of control and elimination interventions.



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.


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.


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.


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.

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


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.


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



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.


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.


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)].


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.


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.



Individual-based models provide modularity and structural flexibility necessary for modeling of infectious diseases at the within-host and population levels, but are challenging to implement. Levels of complexity can exceed the capacity and timescales for students and trainees in most academic institutions. Here we describe the process and advantages of a multi-disease framework approach developed with formal software support. The epidemiological modeling software, EMOD, has undergone a decade of software development. It is structured so that a majority of code is shared across disease modeling including malaria, HIV, tuberculosis, dengue, polio and typhoid. In additional to implementation efficiency, the sharing increases code usage and testing. The freely available codebase also includes hundreds of regression tests, scientific feature tests and component tests to help verify functionality and avoid inadvertent changes to functionality during future development. Here we describe the levels of detail, flexible configurability and modularity enabled by EMOD and the role of software development principles and processes in its development.

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


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.

Kat S Rock, Martial L Ndeffo-Mbah, Soledad Castaño, Cody Palmer, Abhishek Pandey, Katherine E Atkins, Joseph M Ndung’u, T Déirdre Hollingsworth, Alison Galvani, Caitlin Bever, Nakul Chitnis, Matt J Keeling



Control of gambiense sleeping sickness relies predominantly on passive and active screening of people, followed by treatment.


Mathematical modeling explores the potential of 3 complementary interventions in high- and low-transmission settings.


Intervention strategies that included vector control are predicted to halt transmission most quickly. Targeted active screening, with better and more focused coverage, and enhanced passive surveillance, with improved access to diagnosis and treatment, are both estimated to avert many new infections but, when used alone, are unlikely to halt transmission before 2030 in high-risk settings.


There was general model consensus in the ranking of the 3 complementary interventions studied, although with discrepancies between the quantitative predictions due to differing epidemiological assumptions within the models. While these predictions provide generic insights into improving control, the most effective strategy in any situation depends on the specific epidemiology in the region and the associated costs.