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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.

John M. Marshall, Sean L. Wu, Hector M. Sanchez C., Samson S. Kiware, Micky Ndhlovu, André Lin Ouédraogo, Mahamoudou B. Touré, Hugh J. Sturrock, Azra C. Ghani, Neil M. Ferguson


As Africa-wide malaria prevalence declines, an understanding of human movement patterns is essential to inform how best to target interventions. We fitted movement models to trip data from surveys conducted at 3–5 sites throughout each of Mali, Burkina Faso, Zambia and Tanzania. Two models were compared in terms of their ability to predict the observed movement patterns – a gravity model, in which movement rates between pairs of locations increase with population size and decrease with distance, and a radiation model, in which travelers are cumulatively “absorbed” as they move outwards from their origin of travel. The gravity model provided a better fit to the data overall and for travel to large populations, while the radiation model provided a better fit for nearby populations. One strength of the data set was that trips could be categorized according to traveler group – namely, women traveling with children in all survey countries and youth workers in Mali. For gravity models fitted to data specific to these groups, youth workers were found to have a higher travel frequency to large population centers, and women traveling with children a lower frequency. These models may help predict the spatial transmission of malaria parasites and inform strategies to control their spread.


Malaria transmission remains high in Sub-Saharan Africa despite large-scale implementation of malaria control interventions. A comprehensive understanding of the transmissibility of infections to mosquitoes may guide the design of more effective transmission reducing strategies. The impact of P. falciparum sexual stage immunity on the infectious reservoir for malaria has never been studied in natural settings. Repeated measurements were carried out at start-wet, peak-wet and dry season, and provided data on antibody responses against gametocyte/gamete antigens Pfs48/45 and Pfs230 as anti-gametocyte immunity. Data on high and low-density infections and their infectiousness to anopheline mosquitoes were obtained using quantitative molecular methods and mosquito feeding assays, respectively. An event-driven model for P. falciparum sexual stage immunity was developed and fit to data using an agent based malaria model infrastructure. We found that Pfs48/45 and Pfs230 antibody densities increased with increasing concurrent gametocyte densities; associated with 55–70% reduction in oocyst intensity and achieved up to 44% reduction in proportions of infected mosquitoes. We showed that P. falciparum sexual stage immunity significantly reduces transmission of microscopic (p < 0.001) but not submicroscopic (p = 0.937) gametocyte infections to mosquitoes and that incorporating sexual stage immunity into mathematical models had a considerable impact on the contribution of different age groups to the infectious reservoir of malaria. Human antibody responses to gametocyte antigens are likely to be dependent on recent and concurrent high-density gametocyte exposure and have a pronounced impact on the likelihood of onward transmission of microscopic gametocyte densities compared to low density infections. Our mathematical simulations indicate that anti-gametocyte immunity is an important factor for predicting and understanding the composition and dynamics of the human infectious reservoir for malaria.


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.

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



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.


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.


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.


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.



Mass drug administration (MDA) is a control and elimination tool for treating infectious diseases. For malaria, it is widely accepted that conducting MDA during the dry season results in the best outcomes. However, seasonal movement of populations into and out of MDA target areas is common in many places and could potentially fundamentally limit the ability of MDA campaigns to achieve elimination.


A mathematical model was used to simulate malaria transmission in two villages connected to a high-risk area into and out of which 10% of villagers traveled seasonally. MDA was given only in the villages. Prevalence reduction under various possible timings of MDA and seasonal travel was predicted.


MDA is most successful when distributed outside the traveling season and during the village low-transmission season. MDA is least successful when distributed during the traveling season and when traveling overlaps with the peak transmission season in the high-risk area. Mistiming MDA relative to seasonal travel resulted in much poorer outcomes than mistiming MDA relative to the peak transmission season within the villages.


Seasonal movement patterns of high-risk groups should be taken into consideration when selecting the optimum timing of MDA campaigns.


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.