Cost-effective control of chronic viral diseases: Finding the optimal level of screening and contact tracing

Chronic viral diseases such as human immunodeficiency virus (HIV) and hepatitis B virus (HBV) afflict millions of people worldwide. A key public health challenge in managing such diseases is identifying infected, asymptomatic individuals so that they can receive antiviral treatment. Such treatment can benefit both the treated individual (by improving quality and length of life) and the population as a whole (through reduced transmission). We develop a compartmental model of a chronic, treatable infectious disease and use it to evaluate the cost and effectiveness of different levels of screening and contact tracing. We show that: (1) the optimal strategy is to get infected individuals into treatment at the maximal rate until the incremental health benefits balance the incremental cost of controlling the disease; (2) as one reduces the disease prevalence by moving people into treatment (which decreases the chance that they will infect others), one should increase the level of contact tracing to compensate for the decreased effectiveness of screening; (3) as the disease becomes less prevalent, it is optimal to spend more per case identified; and (4) the relative mix of screening and contact tracing at any level of disease prevalence is such that the marginal efficiency of contact tracing (cost per infected person found) equals that of screening if possible (e.g., when capacity limitations are not binding). We also show how to determine the cost-effective equilibrium level of disease prevalence (among untreated individuals), and we develop an approximation of the path of the optimal prevalence over time. Using this, one can obtain a close approximation of the optimal solution without having to solve an optimal control problem. We apply our methods to an example of hepatitis B virus.     

Sexually transmitted disease and the evolution of mating systems

Sexually transmitted diseases (STDs) have been shown to increase the costs of multiple mating and therefore favor relatively monogamous mating strategies. We examine another way in which STDs can influence mating systems in species in which female choice is important. Because more popular males are more likely to become infected, STDs can counteract any selective pressure that generates strong mating skews. We build two models to investigate female mate choice when the sexual behavior of females determines the prevalence of infection in the population. The first model has no explicit social structure. The second model considers the spatial distribution of matings under social monogamy, when females mated to unattractive males seek extrapair fertilizations from attractive males. In both cases, the STD has the potential to drastically reduce the mating skew. However, this reduction does not always happen. If the per contact transmission probability is low, the disease dies out and is of no consequence. In contrast, if the transmission probability is very high, males are likely to be infected regardless of their attractiveness, and mating with the most attractive males imposes again no extra cost for the female. We also show that optimal female responses to the risk of STDs can buffer the prevalence of infection to remain constant, or even decrease, with increasing per contact transmission probabilities. In all cases considered, the feedback between mate choice strategies and STD prevalence creates frequency-dependent fitness benefits for the two alternative female phenotypes considered (choosy vs. randomly mating females or faithful vs. unfaithful females). This maintains mixed evolutionarily stable strategies or polymorphisms in female behavior. In this way, a sexually transmitted disease can stabilize the populationwide proportion of females that mate with the most attractive males or that seek extrapair copulations.     

EPICE-HIV: An Epidemiologic Cost-Effectiveness Model for HIV Treatment

The goal of this research was to establish a new and innovative framework for cost-effectiveness modeling of HIV-1 treatment, simultaneously considering both clinical and epidemiological outcomes. EPICE-HIV is a multi-paradigm model based on a within-host micro-simulation model for the disease progression of HIV-1 infected individuals and an agent-based sexual contact network (SCN) model for the transmission of HIV-1 infection. It includes HIV-1 viral dynamics, CD4⁺ T cell infection rates, and pharmacokinetics/pharmacodynamics modeling. Disease progression of HIV-1 infected individuals is driven by the interdependent changes in CD4⁺ T cell count, changes in plasma HIV-1 RNA, accumulation of resistance mutations and adherence to treatment. The two parts of the model are joined through a per-sexual-act and viral load dependent probability of disease transmission in HIV-discordant couples. Internal validity of the disease progression part of the model is assessed and external validity is demonstrated in comparison to the outcomes observed in the STaR randomized controlled clinical trial. We found that overall adherence to treatment and the resulting pattern of treatment interruptions are key drivers of HIV-1 treatment outcomes. Our model, though largely independent of efficacy data from RCT, was accurate in producing 96-week outcomes, qualitatively and quantitatively comparable to the ones observed in the STaR trial. We demonstrate that multi-paradigm micro-simulation modeling is a promising tool to generate evidence about optimal policy strategies in HIV-1 treatment, including treatment efficacy, HIV-1 transmission, and cost-effectiveness analysis.     

The effects of population structure on the spread of the HIV infection

A model for the spread of human immunodeficiency virus (HIV) in a population of male homosexuals is presented. The population is divided into five groups on the basis of degree of sexual activity. Within each group, the individuals are classified as 1) susceptible; 2) infective; or 3) removed because of a lack of sexual activity associated with advanced acquired immunodeficiency disease (AIDS). The infective individuals are further subdivided into four stages of infection. Analyses of the model address two questions with regard to the spread of HIV: (1) What is the effect of level of sexual activity on an individual's risk for infection, and (2) What is the effect that assumptions about mixing between groups have on both individual risk and transmission throughout a population? Results from analyses using a number of different parameter estimates show that increased levels of sexual activity increase the likelihood that an individual will become infected. In addition, the initial spread of the disease is markedly affected by variation in the amount of contact among individuals from different subpopulations. The steady-state incidence of the disease is not markedly affected by variation in the contact patterns, but the size of the steady-state population and therefore the proportion of infected individuals in the population does vary significantly with changes in the degree of mixing among subpopulations. These results show clearly the sensitivity of model outcomes to variation in the patterns of contact among individuals and the need for better data on such interactions to aid in understanding and predicting the spread of HIV.     

A stochastic model for the development of an AIDS epidemic in a heterosexual population.

A non-age-dependent model, describing the evolution of a bisexual population, is developed in this paper and applied to projecting an AIDS epidemic in a heterosexual population. Included in the formulation are frequency- and non-frequency-dependent rules of partnership formation as well as five states of HIV disease, affecting the probability of infection per sexual contact. Results from computer experiments, designed to study the development of an AIDS epidemic in a heterosexual population fed by single males with a 50% prevalence of HIV infection prior to becoming active in heterosexual partnerships, are reported. In these experiments, the only source of HIV infection for females was sexual contacts with infected males within partnerships. Data on the probability of infection per sexual contact with an infected partner and the number of sexual contacts per month were incorporated into the model. However, the numbers used for the initial population of singles, couples, and those becoming sexually active per month were hypothetical. Even though the prevalence of HIV infection among males entering heterosexual partnerships was high, after 30 years the projected prevalence of HIV infection among females ranged from about 10 to 15% depending in part on the expected duration of partnerships and on whether the frequency- or non-frequency-dependent model was used. In these experiments, solutions of the embedded, nonlinear, deterministic equations for the incidence of HIV infection and the cumulative number of deaths due to AIDS proved to be good measures of central tendency for the sample functions of the stochastic population process.     

A General HIV Incidence Inference Scheme Based on Likelihood of Individual Level Data and a Population Renewal Equation

We derive a new method to estimate the age specific incidence of an infection with a differential mortality, using individual level infection status data from successive surveys. The method consists of a) an SI-type model to express the incidence rate in terms of the prevalence and its derivatives as well as the difference in mortality rate, and b) a maximum likelihood approach to estimate the prevalence and its derivatives. Estimates can in principle be obtained for any chosen age and time, and no particular assumptions are made about the epidemiological or demographic context. This is in contrast with earlier methods for estimating incidence from prevalence data, which work with aggregated data, and the aggregated effect of demographic and epidemiological rates over the time interval between prevalence surveys. Numerical simulation of HIV epidemics, under the presumption of known excess mortality due to infection, shows improved control of bias and variance, compared to previous methods. Our analysis motivates for a) effort to be applied to obtain accurate estimates of excess mortality rates as a function of age and time among HIV infected individuals and b) use of individual level rather than aggregated data in order to estimate HIV incidence rates at times between two prevalence surveys.     

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.     

Healthcare-Associated <Emphasis Type="Italic">Clostridium difficile</Emphasis> Infections are Sustained by Disease from the Community

Clostridium difficile infections (CDIs) are some of the most common hospital-associated infections worldwide. Approximately 5% of the general population is colonised with the pathogen, but most are protected from disease by normal intestinal flora or immune responses to toxins. We developed a stochastic compartmental model of CDI in hospitals that captures the condition of the host’s gut flora and the role of adaptive immune responses. A novel, derivative-based method for sensitivity analysis of individual-level outcomes was developed and applied to the model. The model reproduced the observed incidence and recurrence rates for hospitals with high and moderate incidence of hospital-acquired CDI. In both scenarios, the reproduction number for within-hospital transmission was less than 1 (0.67 and 0.44, respectively), but the proportion colonised with C. difficile at discharge (7.3 and 6.1%, respectively) exceeded the proportion colonised at admission (5%). The transmission and prevalence of CDI were most sensitive to the average length of stay and the transmission rate of the pathogen. Recurrent infections were most strongly affected by the treatment success rate and the immune profile of patients. Transmission within hospitals is substantial and leads to a net export of colonised individuals to the broader community. However, within-hospital transmission alone is insufficient to sustain endemic conditions in hospitals without the constant importation of colonised individuals. Improved hygiene practices to reduce transmission from symptomatic and asymptomatic individuals and reduced length of stay are most likely to reduce within-hospital transmission and infections; however, these interventions are likely to have a smaller effect on the probability of recurrence. Immunising inpatients against the toxins produced by C. difficile will reduce the incidence of CDI but may increase transmission.     

The effect of predation on the prevalence and aggregation of pathogens in prey

Although pathogens and predators have been widely used as bio-control agents against problematic prey species, little has been done to examine the prevalence and aggregation of pathogens in spatially structured eco-epidemiological systems. Here, we present a spatial model of a predator-prey/host-parasite system based on pair approximation and spatially stochastic simulations, with the predation pressure indicated by predator abundance and predation rates. Susceptible prey can not only be infected by contacting adjacent infected individuals but also by the global transmission of pathogens. The disease prevalence was found to follow a hump-shaped function in response to predation pressure. Moreover, predation pressure was not always negatively correlated with pathogen aggregation as proposed from empirical studies, but depending on the level of predation pressure. Highly connected site network facilitated the parasites infection, especially under high predation pressure. However, the connectivity of site network had no effect on the prevalence and aggregation of pathogens that can infect health prey through global transmission. It is thus possible to better design biological control strategies for target species by manipulating predation pressure and the range of pathogen transmission.     

Predicting the impact of a nonsterilizing vaccine against human immunodeficiency virus

Studies of human immunodeficiency virus (HIV) vaccines in animal models suggest that it is difficult to induce complete protection from infection (sterilizing immunity) but that it is possible to reduce the viral load and to slow or prevent disease progression following infection. We have developed an age-structured epidemiological model of the effects of a disease-modifying HIV vaccine that incorporates the intrahost dynamics of infection, a transmission rate and host mortality that depend on the viral load, the possible evolution and transmission of vaccine escape mutant viruses, a finite duration of vaccine protection, and possible changes in sexual behavior. Using this model, we investigated the long-term outcome of a disease-modifying vaccine and utilized uncertainty analysis to quantify the effects of our lack of precise knowledge of various parameters. Our results suggest that the extent of viral load reduction in vaccinated infected individuals (compared to unvaccinated individuals) is the key predictor of vaccine efficacy. Reductions in viral load of about 1 log(10) copies ml(-1) would be sufficient to significantly reduce HIV-associated mortality in the first 20 years after the introduction of vaccination. Changes in sexual risk behavior also had a strong impact on the epidemic outcome. The impact of vaccination is dependent on the population in which it is used, with disease-modifying vaccines predicted to have the most impact in areas of low prevalence and rapid epidemic growth. Surprisingly, the extent to which vaccination alters disease progression, the rate of generation of escape mutants, and the transmission of escape mutants are predicted to have only a weak impact on the epidemic outcome over the first 25 years after the introduction of a vaccine.     

On the transmission of HIV with self-protective behavior and preferred mixing

An epidemic model of HIV transmission with self-protective behavior and preferred mixing is presented. Individuals in the model are assumed to choose their levels of risk behavior by comparing the costs and benefits of self-protective actions. Unlike in models which treat individual risk behavior as exogenously given and fixed, the condition under which an endemic steady state equilibrium exists does not depend on the extent of assortative mixing in the population. Specifically, a unique endemic equilibrium exists when the basic reproductive number of the disease, which is given in the model by the expected number of secondary infections caused by an infected individual in the absence of any self-protection, is strictly greater than one. Otherwise, the disease-free equilibrium is the only steady state equilibrium. With respect to changes in contact patterns, it is shown that, if the degree of preferred mixing is increased, the disease prevalence can decrease in the high-risk subpopulation consisting of individuals who are more likely to engage in unsafe practices. The situation is reversed for the low-risk subpopulation, which is composed of individuals who are less willing to engage in risky practices, so that increasing the likelihood of mixing with members of one's own group may increase the prevalence level within the low-risk subpopulation.     

Frequency-dependent incidence in models of sexually transmitted diseases: portrayal of pair-based transmission and effects of illness on contact behaviour

We explore the transmission process for sexually transmitted diseases (STDs). We derive the classical frequency-dependent incidence mechanistically from a pair-formation model, using an approximation that applies to populations with rapid pairing dynamics (such as core groups or non-pair-bonding animals). This mechanistic derivation provides a framework to assess how accurately frequency-dependent incidence portrays the pair-based transmission known to underlie STD dynamics. This accuracy depends strongly on the disease being studied: frequency-dependent formulations are more suitable for chronic less-transmissible infections than for transient highly transmissible infections. Our results thus support earlier proposals to divide STDs into these two functional classes, and we suggest guidelines to help assess under what conditions each class can be appropriately modelled using frequency-dependent incidence. We then extend the derivation to include situations where infected individuals exhibit altered pairing behaviour. For four cases of increasing behavioural complexity, analytic expressions are presented for the generalized frequency-dependent incidence rate, basic reproductive number (R0) and steady-state prevalence (i infinity) of an epidemic. The expression for R0 is identical for all cases, giving refined insights into determinants of invasibility of STDs. Potentially significant effects of infection-induced changes in contact behaviour are illustrated by simulating epidemics of bacterial and viral STDs. We discuss the application of our results to STDs (in humans and animals) and other infectious diseases.     

Optimal strategy for controlling the spread of HIV/AIDS disease: a case study of South Africa

HIV/AIDS disease continues to spread alarmingly despite the huge amounts of resources invested in fighting it. There is a need to integrate the series of control measures available to ensure a consistent reduction in the incidence of the disease pending the discovery of its cure. We present a deterministic model for controlling the spread of the disease using change in sexual habits and antiretroviral (ARV) therapy as control measures. We formulate a fixed time optimal control problem subject to the model dynamics with the goal of finding the optimal combination of the two control measures that will minimize the cost of the control efforts as well as the incidence of the disease. We estimate the model state initial conditions and parameter values from the demographic and HIV/AIDS data of South Africa. We use Pontryagin's maximum principle to derive the optimality system and solve the system numerically. Compared with the practice in most resource-limited settings where ARV treatment is given only to patients with full-blown AIDS, our simulation results suggest that starting the treatment as soon as the patients progress to the pre-AIDS stage of the disease coupled with appreciable change in the susceptible individuals’ sexual habits reduces both the incidence and prevalence of the disease faster. In fact, the results predict that the implementation of the proposed strategy would drive new cases of the disease towards eradication in 10 years.     

一类人禽间传染病模型的动力学分析

讨论了一类人禽传染病模型,其中禽类被病毒感染后人们采取措施治疗病禽．治疗有助于禽类的存活,但人们可能通过接触病禽而被感染．禽间的疾病传播服从饱和接触率函数,人与禽的接触服从线性接触率．完成了稳定性和持久性研究,且进行了数值模拟以评估治疗的效果和风险．     

Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model

We perform sensitivity analyses on a mathematical model of malaria transmission to determine the relative importance of model parameters to disease transmission and prevalence. We compile two sets of baseline parameter values: one for areas of high transmission and one for low transmission. We compute sensitivity indices of the reproductive number (which measures initial disease transmission) and the endemic equilibrium point (which measures disease prevalence) to the parameters at the baseline values. We find that in areas of low transmission, the reproductive number and the equilibrium proportion of infectious humans are most sensitive to the mosquito biting rate. In areas of high transmission, the reproductive number is again most sensitive to the mosquito biting rate, but the equilibrium proportion of infectious humans is most sensitive to the human recovery rate. This suggests strategies that target the mosquito biting rate (such as the use of insecticide-treated bed nets and indoor residual spraying) and those that target the human recovery rate (such as the prompt diagnosis and treatment of infectious individuals) can be successful in controlling malaria.     

Type-Specific Human Papillomavirus Biological Features: Validated Model-Based Estimates

Infection with high-risk (hr) human papillomavirus (HPV) is considered the necessary cause of cervical cancer. Vaccination against HPV16 and 18 types, which are responsible of about 75% of cervical cancer worldwide, is expected to have a major global impact on cervical cancer occurrence. Valid estimates of the parameters that regulate the natural history of hrHPV infections are crucial to draw reliable projections of the impact of vaccination. We devised a mathematical model to estimate the probability of infection transmission, the rate of clearance, and the patterns of immune response following the clearance of infection of 13 hrHPV types. To test the validity of our estimates, we fitted the same transmission model to two large independent datasets from Italy and Sweden and assessed finding consistency. The two populations, both unvaccinated, differed substantially by sexual behaviour, age distribution, and study setting (screening for cervical cancer or Chlamydia trachomatis infection). Estimated transmission probability of hrHPV types (80% for HPV16, 73%-82% for HPV18, and above 50% for most other types); clearance rates decreasing as a function of time since infection; and partial protection against re-infection with the same hrHPV type (approximately 20% for HPV16 and 50% for the other types) were similar in the two countries. The model could accurately predict the HPV16 prevalence observed in Italy among women who were not infected three years before. In conclusion, our models inform on biological parameters that cannot at the moment be measured directly from any empirical data but are essential to forecast the impact of HPV vaccination programmes.     

A general model for the influence of immune priming on disease prevalence

Invertebrate immune priming, and other forms of innate immune memory in bacteria, plants, and mammals, modulate the post‐infection resistance, tolerance, and survival phenotypes of individuals previously exposed to microbes. By influencing the probability of both transmission and disease‐induced mortality, priming is likely to have a significant impact on disease dynamics. Two alternative models have been proposed as frameworks for the role of priming in infected populations, but the differences in their underlying key assumptions yield very different predictions for the effect of priming on disease dynamics. By examining these assumptions from the lens of within‐host dynamics, the model presented in this paper demonstrates that priming systems can be characterized along a continuous dose‐response gradient that unites these disparate frameworks. Moreover, it facilitates the incorporation of different kinds of immunological plasticity mechanisms, as well as the exposure probability and transmission characteristics of parasites. Simulating the interaction of these thresholds with the diversity of parasite life history strategies and distributions predicts that priming may actually inflate disease prevalence under certain conditions. Thus, priming of innate immune systems may act analogously to leaky vaccines and drive parasite virulence evolution. The results underscore the need for experimental studies that determine dose response curves for the both the probability of becoming primed following primary parasite exposure and shifts in resistance and tolerance in infected primed hosts. This framework is applicable to a variety of systems that show immunological memory.     

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.     

Mathematical model for Zika virus dynamics with sexual transmission route

Zika virus is a flavivirus transmitted to humans primarily through the bite of infected Aedes mosquitoes. In addition to vector-borne spread, however, the virus can also be transmitted through sexual contact. In this paper, we formulate and analyze a new system of ordinary differential equations which incorporates both vector and sexual transmission routes. Theoretical analysis of this model when there is no disease induced mortality shows that the disease-free equilibrium is locally and globally asymptotically stable whenever the associated reproduction number is less than unity and unstable otherwise. However, when we extend this same model to include Zika induced mortality, which have been documented in Latin America, we find that the model exhibits a backward bifurcation. Specifically, a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. To further explore model predictions, we use numerical simulations to assess the importance of sexual transmission to disease dynamics. This analysis shows that risky behavior involving multiple sexual partners, particularly among male populations, substantially increases the number of infected individuals in the population, contributing significantly to the disease burden in the community.