PopART-IBM,a highly efficient stochastic individual-based simulation model of generalised HIV epidemics developed in the context of the HPTN 071 (PopART) trial

Mathematical models are powerful tools in HIV epidemiology, producing quantitative projections of key indicators such as HIV incidence and prevalence. In order to improve the accuracy of predictions, such models need to incorporate a number of behavioural and biological heterogeneities, especially those related to the sexual network within which HIV transmission occurs. An individual-based model, which explicitly models sexual partnerships, is thus often the most natural type of model to choose. In this paper we present PopART-IBM, a computationally efficient individual-based model capable of simulating 50 years of an HIV epidemic in a large, high-prevalence community in under a minute. We show how the model calibrates within a Bayesian inference framework to detailed age- and sex-stratified data from multiple sources on HIV prevalence, awareness of HIV status, ART status, and viral suppression for an HPTN 071 (PopART) study community in Zambia, and present future projections of HIV prevalence and incidence for this community in the absence of trial intervention.     

Resolving discrepancies between deterministic population models and individual-based simulations

ABSTRACT This work ties together two distinct modeling frameworks for population dynamics: an individual-based simulation and a set of coupled integrodifferential equations involving population densities. The simulation model represents an idealized predator-prey system formulated at the scale of discrete individuals, explicitly incorporating their mutual interactions, whereas the population-level framework is a generalized version of reaction-diffusion models that incorporate population densities coupled to one another by interaction rates. Here I use various combinations of long-range dispersal for both the offspring and adult stages of both prey and predator species, providing a broad range of spatial and temporal dynamics, to compare and contrast the two model frameworks. Taking the individual-based modeling results as given, two examinations of the reaction-dispersal model are made: linear stability analysis of the deterministic equations and direct numerical solution of the model equations. I also modify the numerical solution in two ways to account for the stochastic nature of individual-based processes, which include independent, local perturbations in population density and a minimum population density within integration cells, below which the population is set to zero. These modifications introduce new parameters into the population-level model, which I adjust to reproduce the individual-based model results. The individual-based model is then modified to minimize the effects of stochasticity, producing a match of the predictions from the numerical integration of the population-level model without stochasticity.     

Intimate Injection Partnerships Are at Elevated Risk of High-Risk Injecting: A Multi-Level Longitudinal Study of HCV-Serodiscordant Injection Partnerships in San Francisco,CA

Background

It is increasingly recognized that the risk for HIV and hepatitis C (HCV) transmission among people who inject drugs (PWID), such as syringe sharing, occurs in the context of relationships between (at least) two people. Evidence suggests that the risk associated with injection behavior varies with injection partner types.

Methods

We utilized longitudinal dyad-level data from a study of young PWID from San Francisco (2006 to 2013) to investigate the relationship-level factors influencing high-risk injecting within HCV-serodiscordant injection partners (i.e., individuals who injected together ≥5 times in the prior month). Utilizing data from 70 HCV-serodiscordant injection partnerships, we used generalized linear models to examine relationship-level predictors (i.e., partnership composition, partnership closeness, and partnership dynamics) of: (1) receptive syringe sharing (RSS); and (2) receptive cooker use (RCU), as reported by the HCV-negative injection partner.

Results

As reported by the “at-risk” HCV-negative injection partner, receptive syringe sharing (RSS) and receptive cooker use (RCU) were 19% and 33% at enrollment, and 11% and 12% over all visits (total follow-up time 55 person-years) resulting in 13 new HCV-infections (incidence rate: 23.8/100 person-years). Person-level factors, injection partnership composition, and partnership dynamics were not significantly associated with either RSS or RCU. Instead, intimate injection partnerships (those who lived together and were also in a sexual relationship) were independently associated with a 5-times greater risk of both RSS and a 7-times greater risk of RCU when compared to injecting only partnerships.

Conclusion

Our findings suggest a positive, and amplified effect of relationship factors on injecting drug risk behaviors among young PWID injection partnerships. The majority of interventions to reduce injection drug use related harms focus on individual-based education to increase drug use knowledge. Our findings support the need to expand harm reduction strategies to relationship-based messaging and interventions.     

The influence of concurrent partnerships on the dynamics of HIV/AIDS.

Most models of the spread of HIV/AIDS assume that the probability of transmission from an infected individual to a susceptible partner has some constant value per sexual act, compounding independently randomly (so that ten acts with one person chosen from a particular group has, on average, the same risk as one act with each of ten different people from that group). Guided by available data, other models treat the transmission process as being some characteristic (but highly variable) value per partnership, independent of the number of acts. This latter approach does not allow for the possible effects of concurrent partnerships, and therefore does not take account of the possibility that an initially uninfected partner of a given susceptible individual may become infected over the duration of their partnership. We present a new model, based on transmission per partnership, that takes account of partnership duration. If the number of overlapping partnerships is high enough (so that R0 greater than 1 among "standing crops" of partners), any initial infection will spread very fast--on the time scale of a few times the latent interval (a few months)--among existing networks of partners. After this initial "fast phase," the subsequent epidemic proceeds more slowly along conventional lines as new partnerships are formed. These properties of the model are illustrated numerically and by analytic studies (using singular perturbation theory). The possibility of such "two time-scale" phenomena could have implications for data analysis based on statistical back-projection.     

Intraguild predation with spatially structured interactions

Consumer–resource interactions with intraguild predation (IGP) were studied in a spatial setting (i.e., predators catch prey and individuals reproduce within local neighborhoods only). Pair approximation (a method for deriving ordinary differential equations that approximate the dynamics of a community that interacts in a lattice environment) was used to study the effect of spatially structured species interactions. An individual-based computer simulation was used to extend the study to a case with spatially variable resource densities. The qualitative results of the pair approximation model were similar to those of the corresponding non-spatial model. However, the spatial model predicted coex((istence over a wider range of parameters than the non-spatial model when intraguild prey are nutritionally valuable to intraguild predators. Spatially heterogeneous resource distributions and spatially structured interaction could overturn the qualitative predictions of non-spatial models.     

Modelling Direct Radiation and Canopy Gap Regimes in Tropical Forests

Spatial and temporal variation in the below‐canopy light environment of tropical forests is not well known and its measurement is technically challenging. Distributions of gap and understory areas in forests are likewise little known because of the resource requirements of forest structural censuses and a lack of consensus over how gaps should be defined. A basic model of forest structure, based on tree allometries from the 50 ha Forest Dynamics Plot on Barro Colorado Island (BCI), Panama, and a solar positioning algorithm were used to predict spatial and temporal variation in the distribution of direct light at the forest floor. Predicted duration of direct sunlight was then compared with the distribution of gap and understory areas, delimited according to four standard gap definitions, giving predictions for the correspondence between direct light regimes and forest structure. At least 36 percent of the areas of gaps of all sizes was predicted to receive < 1 h of direct sunlight per day, and the understory to receive direct sunlight for ≥ 1 h per day in up to 15 percent of its area, even when not in proximity to gaps. The predicted distribution of light changed over the course of the year with the greatest spread of light throughout the forest floor coinciding with the months when maximum daily solar elevation peaked. These predictions suggest a partial decoupling of light regimes from canopy structure, with implications for gap definitions, patch models of forest development and current understanding of tree seedling recruitment patterns.     

HIV Status Awareness,Partnership Dissolution and HIV Transmission in Generalized Epidemics

Objectives

HIV status aware couples with at least one HIV positive partner are characterized by high separation and divorce rates. This phenomenon is often described as a corollary of couples HIV Testing and Counseling (HTC) that ought to be minimized. In this contribution, we demonstrate the implications of partnership dissolution in serodiscordant couples for the propagation of HIV.

Methods

We develop a compartmental model to study epidemic outcomes of elevated partnership dissolution rates in serodiscordant couples and parameterize it with estimates from population-based data (Rakai, Uganda).

Results

Via its effect on partnership dissolution, every percentage point increase in HIV status awareness reduces HIV incidence in monogamous populations by 0.27 percent for women and 0.63 percent for men. These effects are even larger when the assumption of monogamy can be relaxed, but are moderated by other behavior changes (e.g., increased condom use) in HIV status aware serodiscordant partnerships. When these behavior changes are taken into account, each percentage point increase in HIV status awareness reduces HIV incidence by 0.13 and 0.32 percent for women and men, respectively (assuming monogamy). The partnership dissolution effect exists because it decreases the fraction of serodiscordant couples in the population and prolongs the time that individuals spend outside partnerships.

Conclusion

Our model predicts that elevated partnership dissolution rates in HIV status aware serodiscordant couples reduce the spread of HIV. As a consequence, the full impact of couples HTC for HIV prevention is probably larger than recognized to date. Particularly high partnership dissolution rates in female positive serodiscordant couples contribute to the gender imbalance in HIV infections.     

Epidemiological models for sexually transmitted diseases

The classical models for sexually transmitted infections assume homogeneous mixing either between all males and females or between certain subgroups of males and females with heterogeneous contact rates. This implies that everybody is all the time at risk of acquiring an infection. These models ignore the fact that the formation of a pair of two susceptibles renders them in a sense temporarily immune to infection as long as the partners do not separate and have no contacts with other partners. The present paper takes into account the phenomenon of pair formation by introducing explicitly a pairing rate and a separation rate. The infection transmission dynamics depends on the contact rate within a pair and the duration of a partnership. It turns out that endemic equilibria can only exist if the separation rate is sufficiently large in order to ensure the necessary number of sexual partners. The classical models are recovered if one lets the separation rate tend to infinity.This work has been supported by Deutsche Forschungsgemeinschaft     

Development,Calibration and Performance of an HIV Transmission Model Incorporating Natural History and Behavioral Patterns: Application in South Africa

Understanding HIV transmission dynamics is critical to estimating the potential population-wide impact of HIV prevention and treatment interventions. We developed an individual-based simulation model of the heterosexual HIV epidemic in South Africa and linked it to the previously published Cost-Effectiveness of Preventing AIDS Complications (CEPAC) International Model, which simulates the natural history and treatment of HIV. In this new model, the CEPAC Dynamic Model (CDM), the probability of HIV transmission per sexual encounter between short-term, long-term and commercial sex worker partners depends upon the HIV RNA and disease stage of the infected partner, condom use, and the circumcision status of the uninfected male partner. We included behavioral, demographic and biological values in the CDM and calibrated to HIV prevalence in South Africa pre-antiretroviral therapy. Using a multi-step fitting procedure based on Bayesian melding methodology, we performed 264,225 simulations of the HIV epidemic in South Africa and identified 3,750 parameter sets that created an epidemic and had behavioral characteristics representative of a South African population pre-ART. Of these parameter sets, 564 contributed 90% of the likelihood weight to the fit, and closely reproduced the UNAIDS HIV prevalence curve in South Africa from 1990–2002. The calibration was sensitive to changes in the rate of formation of short-duration partnerships and to the partnership acquisition rate among high-risk individuals, both of which impacted concurrency. Runs that closely fit to historical HIV prevalence reflect diverse ranges for individual parameter values and predict a wide range of possible steady-state prevalence in the absence of interventions, illustrating the value of the calibration procedure and utility of the model for evaluating interventions. This model, which includes detailed behavioral patterns and HIV natural history, closely fits HIV prevalence estimates.     

Estimation of cat medial gastrocnemius fascicle lengths during dynamic contractions

In typical muscle models, it is often assumed that the contractile element (fascicle) length depends exclusively on the instantaneous muscle-tendon length and the instantaneous muscle force. In order to test whether the instantaneous fascicle length during dynamic contractions can be predicted from muscle-tendon length and force, fascicle lengths, muscle-tendon lengths, and muscle forces were directly measured in cat medial gastrocnemii during isometric and dynamic contractions. Two theoretical muscle models were developed: model A was based on force-time data obtained during the activation phase and model D on force-time data obtained during the deactivation phase of isometric contractions. To test the models, instantaneous fascicle lengths were predicted from muscle-tendon lengths and forces during dynamic contractions that simulated cat locomotion for speeds ranging from 0.4 to 1.6m/s. The theoretically predicted fascicle lengths were compared with the experimentally measured fascicle lengths. It was found that fascicle lengths were not uniquely associated with muscle-tendon lengths and forces; that is, for a given muscle-tendon length and force, fascicle lengths varied depending on the contractile history. Consequently, models A and D differed in fascicle length predictions; model D (maximum average error=8.5%) was considerably better than model A (maximum average error=22.3%). We conclude from this study that it is not possible to predict the exact fascicle lengths from muscle-tendon lengths and forces alone, however, adequate predictions seem possible based on such a model. The relationship between fascicle length and muscle force and muscle-tendon length is complex and highly non-linear, thus, it appears unlikely that accurate fascicle length predictions can be made without some reference contractions in which fascicle length, muscle-tendon length, and force are measured simultaneously.     

A versatile ODE approximation to a network model for the spread of sexually transmitted diseases

 We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been attempted. Our goals are 1) to investigate issues relating to the application of moment closure approximations to dynamic and irregular networks, and 2) to understand the impact of concurrent casual partnerships on STD transmission through a population of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations. We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic. Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure approximation is very flexible in the kinds of network models it can approximate. Received: 26 August 2001 / Revised version: 15 March 2002 / Published online: 23 August 2002 C.T.B. was supported by the NSF. Key words or phrases: Moment closure approximation – Network model – Pair approximation – Sexually transmitted diseases – Steady/casual partnership network     

Individual-based modelling in ecology: what makes the difference?

Is individual-based modelling really a new approach in ecology? A large part of the uncertainty surrounding this question is a consequence of imprecisely delimited boundaries between classical and individual-based modelling. Genuine 'individual-based' models describe a population made up of individuals that may differ from one another; they also describe changes in numbers of individuals rather than in the population density, and take resource dynamics explicitly into account. Individual-based models that fulfil these criteria will not characterize ecological systems as 'stable' systems in their ideal form, with equilibrium states represented by points in the phase space.     

Egg limitation in host-parasitoid dynamics: an individual-based perspective

Theoretical models of parasitoid-host dynamics predict that egg limitation in parasitoids destabilizes community dynamics. However, although egg limitation is experienced by individual parasitoids with variable success of encountering hosts, such details were neglected in previous models. This study developed an individual-based parasitoid-host model that explicitly incorporates egg limitation and host encounters of individual parasitoids. The model indicates that the combination of egg limitation and variation in the success of encountering hosts stabilizes parasitoid-host dynamics. The stabilizing mechanism emerges from Jensen’s inequality because egg limitation makes the number of offspring inherently concave down in the number of encountered hosts. Reasons for the inconsistent predictions of the effect of egg limitation between the current model and previous models are discussed.     

Relationships between migration rates and landscape resistance assessed using individual-based simulations

Linking landscape effects on gene flow to processes such as dispersal and mating is essential to provide a conceptual foundation for landscape genetics. It is particularly important to determine how classical population genetic models relate to recent individual-based landscape genetic models when assessing individual movement and its influence on population genetic structure. We used classical Wright-Fisher models and spatially explicit, individual-based, landscape genetic models to simulate gene flow via dispersal and mating in a series of landscapes representing two patches of habitat separated by a barrier. We developed a mathematical formula that predicts the relationship between barrier strength (i.e., permeability) and the migration rate (m) across the barrier, thereby linking spatially explicit landscape genetics to classical population genetics theory. We then assessed the reliability of the function by obtaining population genetics parameters (m, F(ST) ) using simulations for both spatially explicit and Wright-Fisher simulation models for a range of gene flow rates. Next, we show that relaxing some of the assumptions of the Wright-Fisher model can substantially change population substructure (i.e., F(ST) ). For example, isolation by distance among individuals on each side of a barrier maintains an F(ST) of ～0.20 regardless of migration rate across the barrier, whereas panmixia on each side of the barrier results in an F(ST) that changes with m as predicted by classical population genetics theory. We suggest that individual-based, spatially explicit modelling provides a general framework to investigate how interactions between movement and landscape resistance drive population genetic patterns and connectivity across complex landscapes.     

Modelling the effects of population structure on childhood disease: the case of varicella

Realistic, individual-based models based on detailed census data are increasingly used to study disease transmission. Whether the rich structure of such models improves predictions is debated. This is studied here for the spread of varicella, a childhood disease, in a realistic population of children where infection occurs in the household, at school, or in the community at large. A methodology is first presented for simulating households with births and aging. Transmission probabilities were fitted for schools and community, which reproduced the overall cumulative incidence of varicella over the age range of 0-11 years old.Moreover, the individual-based model structure allowed us to reproduce several observed features of VZV epidemiology which were not included as hypotheses in the model: the age at varicella in first-born children was older than in other children, in accordance with observation; the same was true for children residing in rural areas. Model predicted incidence was comparable to observed incidence over time. These results show that models based on detailed census data on a small scale provide valid small scale prediction. By simulating several scenarios, we evaluate how varicella epidemiology is shaped by policies, such as age at first school enrolment, and school eviction. This supports the use of such models for investigating outcomes of public health measures.     

Uncertainties in predicting the demographic impact of AIDS

A model giving the demographic impact of AIDS is analysed to examine the sensitivity of the projections when various complicating features are included. The model deals with age and sexual partner change rate as continuous variables and uses a device to specify arbitrary correlations between the ages of the people who form sexual partnerships. The device ensures consistency, in that the amount of partner formation is the same regardless of whether the partnerships are counted from the point of view of males or females. Arbitrary correlation between partner change rate and fertility is also permitted. The results show the uncertainty in model predictions that population growth will reduce over the next 20 years to approximately zero in parts of East Africa severely affected by the AIDS epidemic. The main sources of uncertainty in the model predictions are assumptions concerning the correlation between ages in a partnership, the correlation between partner change rate and fertility, the incubation period of AIDS, and the variability of the female partner change rate.     

How interactions between animal movement and landscape processes modify local range dynamics and extinction risk

Forecasts of range dynamics now incorporate many of the mechanisms and interactions that drive species distributions. However, connectivity continues to be simulated using overly simple distance-based dispersal models with little consideration of how the individual behaviour of dispersing organisms interacts with landscape structure (functional connectivity). Here, we link an individual-based model to a niche-population model to test the implications of this omission. We apply this novel approach to a turtle species inhabiting wetlands which are patchily distributed across a tropical savannah, and whose persistence is threatened by two important synergistic drivers of global change: predation by invasive species and overexploitation. We show that projections of local range dynamics in this study system change substantially when functional connectivity is modelled explicitly. Accounting for functional connectivity in model simulations causes the estimate of extinction risk to increase, and predictions of range contraction to slow. We conclude that models of range dynamics that simulate functional connectivity can reduce an important source of bias in predictions of shifts in species distributions and abundances, especially for organisms whose dispersal behaviours are strongly affected by landscape structure.     

Partnership dynamics and strain competition

Models of epidemic spread that include partnership dynamics within the host population have demonstrated that finite length partnerships can limit the spread of pathogens. Here the influence of partnerships on strain competition is investigated. A simple epidemic and partnership formation model is used to demonstrate that, in contrast to standard epidemiological models, the constraint introduced by partnerships can influence the success of pathogen strains. When partnership turnover is slow, strains must have a long infectious period in order to persist, a requirement of much less importance when partnership turnover is rapid. By introducing a trade-off between transmission rate and infectious period it is shown that populations with different behaviours can favour different strains. Implications for control measures based on behavioural modifications are discussed, with such measures perhaps leading to the emergence of new strains.     

Using a data-constrained model of home range establishment to predict abundance in spatially heterogeneous habitats

Mechanistic modelling approaches that explicitly translate from individual-scale resource selection to the distribution and abundance of a larger population may be better suited to predicting responses to spatially heterogeneous habitat alteration than commonly-used regression models. We developed an individual-based model of home range establishment that, given a mapped distribution of local habitat values, estimates species abundance by simulating the number and position of viable home ranges that can be maintained across a spatially heterogeneous area. We estimated parameters for this model from data on red-backed vole (Myodes gapperi) abundances in 31 boreal forest sites in Ontario, Canada. The home range model had considerably more support from these data than both non-spatial regression models based on the same original habitat variables and a mean-abundance null model. It had nearly equivalent support to a non-spatial regression model that, like the home range model, scaled an aggregate measure of habitat value from local associations with habitat resources. The home range and habitat-value regression models gave similar predictions for vole abundance under simulations of light- and moderate-intensity partial forest harvesting, but the home range model predicted lower abundances than the regression model under high-intensity disturbance. Empirical regression-based approaches for predicting species abundance may overlook processes that affect habitat use by individuals, and often extrapolate poorly to novel habitat conditions. Mechanistic home range models that can be parameterized against abundance data from different habitats permit appropriate scaling from individual- to population-level habitat relationships, and can potentially provide better insights into responses to disturbance.