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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.


Age mixing plays an important role in the formation of relationships within computer simulations of Human Immunodeficiency Virus (HIV) transmission. We present and analyze an algorithm that takes individuals seeking a heterosexual relationship, and forms pairs of a desired joint age mixing distribution. The rate at which eligible individuals seek relationships varies by age group and gender, and is actively manipulated using feedforward and feedback controls to ensure throughput and avoid instability. Theoretical results guarantee that the relationships formed will match the desired joint distribution, in expectation, while simultaneously avoiding throughput problems due to storage and stochastic variations. Results demonstrate the utility and effectiveness of the network generation process within a detailed stochastic agent-based computer model of HIV.


Many questions remain about P. falciparum within-host dynamics, immunity, and transmission–issues that may affect public health campaign planning. These gaps in knowledge concern the distribution of durations of malaria infections, determination of peak parasitemia during acute infection, the relationships among gametocytes and immune responses and infectiousness to mosquitoes, and the effect of antigenic structure on reinfection outcomes. The present model of intra-host dynamics of P. falciparum implements detailed representations of parasite and immune dynamics, with structures based on minimal extrapolations from first-principles biology in its foundations. The model is designed to quickly and readily accommodate gains in mechanistic understanding and to evaluate effects of alternative biological hypothesis through in silico experiments. Simulations follow the parasite from the liver-stage through the detailed asexual cycle to clearance while tracking gametocyte populations. The modeled immune system includes innate inflammatory and specific antibody responses to a repertoire of antigens. The mechanistic focus provides clear explanations for the structure of the distribution of infection durations through the interaction of antigenic variation and innate and adaptive immunity. Infectiousness to mosquitoes appears to be determined not only by the density of gametocytes but also by the level of inflammatory cytokines, which harmonizes an extensive series of study results. Finally, pre-existing immunity can either decrease or increase the duration of infections upon reinfection, depending on the degree of overlap in antigenic repertoires and the strength of the pre-existing immunity.

Jeffrey W. Eaton, Leigh F. Johnson, Joshua A. Salomon, Till Bärnighausen, Eran Bendavid, Anna Bershteyn, David E. Bloom, Valentina Cambiano, Christophe Fraser, Jan A. C. Hontelez, Salal Humair, Daniel J. Klein, Elisa F. Long, Andrew N. Phillips, Carel Pretorius, John Stover, Edward A. Wenger, Brian G. Williams, and Timothy B. Hallett


Many mathematical models have investigated the impact of expanding access to antiretroviral therapy (ART) on new HIV infections. Comparing results and conclusions across models is challenging because models have addressed slightly different questions and have reported different outcome metrics. This study compares the predictions of several mathematical models simulating the same ART intervention programmes to determine the extent to which models agree about the epidemiological impact of expanded ART.

Methods and Findings
Twelve independent mathematical models evaluated a set of standardised ART intervention scenarios in South Africa and reported a common set of outputs. Intervention scenarios systematically varied the CD4 count threshold for treatment eligibility, access to treatment, and programme retention. For a scenario in which 80% of HIV-infected individuals start treatment on average 1 y after their CD4 count drops below 350 cells/µl and 85% remain on treatment after 3 y, the models projected that HIV incidence would be 35% to 54% lower 8 y after the introduction of ART, compared to a counterfactual scenario in which there is no ART. More variation existed in the estimated long-term (38 y) reductions in incidence. The impact of optimistic interventions including immediate ART initiation varied widely across models, maintaining substantial uncertainty about the theoretical prospect for elimination of HIV from the population using ART alone over the next four decades. The number of person-years of ART per infection averted over 8 y ranged between 5.8 and 18.7. Considering the actual scale-up of ART in South Africa, seven models estimated that current HIV incidence is 17% to 32% lower than it would have been in the absence of ART. Differences between model assumptions about CD4 decline and HIV transmissibility over the course of infection explained only a modest amount of the variation in model results.


Mathematical models evaluating the impact of ART vary substantially in structure, complexity, and parameter choices, but all suggest that ART, at high levels of access and with high adherence, has the potential to substantially reduce new HIV infections. There was broad agreement regarding the short-term epidemiologic impact of ambitious treatment scale-up, but more variation in longer term projections and in the efficiency with which treatment can reduce new infections. Differences between model predictions could not be explained by differences in model structure or parameterization that were hypothesized to affect intervention impact.


Antiretroviral treatment (ART) for those infected with HIV can prevent onward transmission of infection, but biological efficacy alone is not enough to guide policy decisions about the role of ART in reducing HIV incidence. Epidemiology, economics, demography, statistics, biology and mathematical modelling will be central in framing key decisions in the optimal use of ART. PLoS Medicine, with the HIV Modelling Consortium, have compiled a set of articles that draws together reactions to the new findings from these perspectives with a forward-looking research agenda. Interlocking themes across those articles are described here. We hope that this collection of articles will provide a foundation upon which greater collaborations between disciplines will be formed, affording deeper insights into these factors that will strengthen the support for evidence-based decision-making in HIV prevention.

Anna Bershteyn, Daniel J. Klein, Edward Wenger, and Philip A. Eckhoff


The expansion of tools against HIV transmission has brought increased interest in epidemiological models that can predict the impact of these interventions. The EMOD-HIV model was recently compared to eleven other independently developed mathematical models of HIV transmission to determine the extent to which they agree about the potential impact of expanded use of antiretroviral therapy in South Africa. Here we describe in detail the modeling methodology used to produce the results in this comparison, which we term EMOD-HIV v0:7. We include a discussion of the structure and a full list of model parameters. We also discuss the architecture of the model, and its potential utility in comparing structural assumptions within a single modeling framework.


Malaria is a major public health issue in much of the world, and the mosquito vectors which drive transmission are key targets for interventions. Mathematical models for planning malaria eradication benefit from detailed representations of local mosquito populations, their natural dynamics and their response to campaign pressures.


A new model is presented for mosquito population dynamics, effects of weather, and impacts of multiple simultaneous interventions. This model is then embedded in a large-scale individual-based simulation and results for local elimination of malaria are discussed. Mosquito population behaviours, such as anthropophily and indoor feeding, are included to study their effect upon the efficacy of vector control-based elimination campaigns.


Results for vector control tools, such as bed nets, indoor spraying, larval control and space spraying, both alone and in combination, are displayed for a single-location simulation with vector species and seasonality characteristic of central Tanzania, varying baseline transmission intensity and vector bionomics. The sensitivities to habitat type, anthropophily, indoor feeding, and baseline transmission intensity are explored.


The ability to model a spectrum of local vector species with different ecologies and behaviours allows local customization of packages of interventions and exploration of the effect of proposed new tools.