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.     

Effects of public health educational campaigns and the role of sex workers on the spread of HIV/AIDS among heterosexuals

This paper presents a sex-structured model for heterosexual transmission of HIV/AIDS in which the population is divided into three subgroups: susceptibles, infectives and AIDS cases. The subgroups are further divided into two classes, consisting of individuals involved in high-risk sexual activities and individuals involved in low-risk sexual activities. The model considers the movement of individuals from high to low sexual activity groups as a result of public health educational campaigns. Thus, in this case public health educational campaigns are resulting in the split of the population into risk groups. The equilibrium and epidemic threshold, which is known as the basic reproductive number (R0), are obtained, and stability (local and global) of the disease-free equilibrium is investigated. The model is extended to incorporate sex workers, and their role in the spread of HIV/AIDS in settings with heterosexual transmission is explored. Comprehensive analytic and numerical techniques are employed in assessing the possible community benefits of public health educational campaigns in controlling HIV/AIDS. From the study, we conclude that the presence of sex workers enlarges the epidemic threshold R0, thus fuels the epidemic among the heterosexuals, and that public health educational campaigns among the high-risk heterosexual population reduces R0, thus can help slow or eradicate the epidemic.     

A multiple decrement fertility table based on parity

This paper is a multivariate generalization of the work of Chiang and van den Berg [Math. Biosci. 62:237-251 (1982)] to model the parity-specific reproductive patterns of female populations using a life table approach. It is also an adaptation of mortality competing risks theory and multiple decrement life tables to the study of parity-specific human fertility. Competing risks in the fertility context are risks of types of reproductive outcome: normal reproductive outcome (type 0); adverse reproductive outcome of type 1; adverse reproductive outcome of type 2; etc. We focus on applicability to studies in demography and reproductive epidemiology involving current populations.     

Dynamics of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells

Stilianakis and Seydel (Bull. Math. Biol., 1999) proposed an ODE model that describes the T-cell dynamics of human T-cell lymphotropic virus I (HTLV-I) infection and the development of adult T-cell leukemia (ATL). Their model consists of four components: uninfected healthy CD4+ T-cells, latently infected CD4+ T-cells, actively infected CD4+ T-cells, and ATL cells. Mathematical analysis that completely determines the global dynamics of this model has been done by Wang et al. (Math. Biosci., 2002). In this note, we first modify the parameters of the model to distinguish between contact and infectivity rates. Then we introduce a discrete time delay to the model to describe the time between emission of contagious particles by active CD4+ T-cells and infection of pure cells. Using the results in Culshaw and Ruan (Math. Biosci., 2000) in the analysis of time delay with respect to cell-free viral spread of HIV, we study the effect of time delay on the stability of the endemically infected equilibrium. Numerical simulations are presented to illustrate the results.     

High risk populations and HIV-1 infection in China

China is currently experiencing one of the most rapidly expanding HIV epidemics in the world. Although the overall prevalence rate is still low, with a population of 1.3 billion, high-risk factors which have contributed to the HIV/AIDS epidemics worldwide continue to prevail in China, including a high rate of injecting drug use and needle sharing, commercial sex with low rates of condom use, and concurrent sex with both commercial sex workers and non-commercial casual or steady sex partners. In addition, there are increasing "double risk" populations overlapping drug users and sex workers, as well as increasing rates of STDs and HIV among high-risk populations. Sexual transmission, therefore, may serve as a bridge connecting high-risk populations with general populations. There is an urgent need to prevent the spread of HIV from these high-risk populations into the general population of China.     

Growth rate and basic reproduction number for population models with a simple periodic factor

For continuous-time population models with a periodic factor which is sinusoidal, both the growth rate and the basic reproduction number are shown to be the largest roots of simple equations involving continued fractions. As an example, we reconsider an SEIS model with a fixed latent period, an exponentially distributed infectious period and a sinusoidal contact rate studied in Williams and Dye [B.G. Williams, C. Dye, Infectious disease persistence when transmission varies seasonally, Math. Biosci. 145 (1997) 77]. We show that apart from a few exceptional parameter values, the epidemic threshold depends not only on the mean contact rate, but also on the amplitude of fluctuations.     

Assessing the effects of drug misuse on HIV/AIDS prevalence

Drug misuse (injecting drug users-IDU) has been recognized to have a significant effect on the spread of HIV/AIDS epidemic. A deterministic model to assess the contribution of drug misuse and sex in the spread of HIV/AIDS is investigated. The threshold parameters of the model are determined and stabilities are analysed. Analysis of the reproduction number has shown that increase in drug misuse results in an increase in HIV infections. Furthermore, numerical simulations of the model show that drug misuse enhances HIV transmission and progression to AIDS. Thus, in a population with intravenous drug users, advocating for safe sex alone will not be enough to control the HIV/AIDS epidemic.     

Global analysis of an SAIS model

This paper is concerned with global analysis of an SAIS epidemiological model in a population of varying size introduced by Busenberg and van den Driessche. In this model the population is divided into three subgroups of susceptible, asymptomatic and infective individuals. It has been shown that this system has no periodic solutions and all its trajectories tend to the equilibria of the system. We use the Poincaré Index theorem to determine the number of the equilibria and their stability properties. We have shown that bistability occurs for suitable values of parameters and found a set of examples of all possible dynamics of the system.     

Fitting the HIV Epidemic in Zambia: A Two-Sex Micro-Simulation Model

Background

In describing and understanding how the HIV epidemic spreads in African countries, previous studies have not taken into account the detailed periods at risk. This study is based on a micro-simulation model (individual-based) of the spread of the HIV epidemic in the population of Zambia, where women tend to marry early and where divorces are not frequent. The main target of the model was to fit the HIV seroprevalence profiles by age and sex observed at the Demographic and Health Survey conducted in 2001.

Methods and Findings

A two-sex micro-simulation model of HIV transmission was developed. Particular attention was paid to precise age-specific estimates of exposure to risk through the modelling of the formation and dissolution of relationships: marriage (stable union), casual partnership, and commercial sex. HIV transmission was exclusively heterosexual for adults or vertical (mother-to-child) for children. Three stages of HIV infection were taken into account. All parameters were derived from empirical population-based data. Results show that basic parameters could not explain the dynamics of the HIV epidemic in Zambia. In order to fit the age and sex patterns, several assumptions were made: differential susceptibility of young women to HIV infection, differential susceptibility or larger number of encounters for male clients of commercial sex workers, and higher transmission rate. The model allowed to quantify the role of each type of relationship in HIV transmission, the proportion of infections occurring at each stage of disease progression, and the net reproduction rate of the epidemic (R ₀ = 1.95).

Conclusions

The simulation model reproduced the dynamics of the HIV epidemic in Zambia, and fitted the age and sex pattern of HIV seroprevalence in 2001. The same model could be used to measure the effect of changing behaviour in the future.     

Spatial patterns in a discrete-time SIS patch model

How do spatial heterogeneity, habitat connectivity, and different movement rates among subpopulations combine to influence the observed spatial patterns of an infectious disease? To find out, we formulated and analyzed a discrete-time SIS patch model. Patch differences in local disease transmission and recovery rates characterize whether patches are low-risk or high-risk, and these differences collectively determine whether the spatial domain, or habitat, is low-risk or high-risk. In low-risk habitats, the disease persists only when the mobility of infected individuals lies below some threshold value, but for high-risk habitats, the disease always persists. When the disease does persist, then there exists an endemic equilibrium (EE) which is unique and positive everywhere. This EE tends to a spatially inhomogeneous disease-free equilibrium (DFE) as the mobility of susceptible individuals tends to zero. The limiting DFE is nonempty on all low-risk patches and it is empty on at least one high-risk patch. Sufficient conditions for the limiting DFE to be empty on other high-risk patches are given in terms of disease transmission and recovery rates, habitat connectivity, and the infected movement rate. These conditions are also illustrated using numerical examples.     

The effects of disease dispersal and host clustering on the epidemic threshold in plants

For an epidemic to occur in a closed population, the transmission rate must be above a threshold level. In plant populations, the threshold depends not only on host density, but on the distribution of hosts in space. This paper presents an alternative analysis of a previously presented stochastic model for an epidemic in continuous space (Bolker, 1999, Bull. Math. Biol. 61, 849–874). A variety of moment closures are investigated to determine the dependence of the epidemic threshold on host spatial distribution and pathogen dispersal. Local correlations that arise during the early phase of the outbreak determine whether a true global epidemic will occur.     

Impact and Cost of the HIV/AIDS National Strategic Plan for Mozambique, 2015-2019—Projections with the Spectrum/Goals Model

Introduction

Mozambique continues to face a severe HIV epidemic and high cost for its control, largely born by international donors. We assessed feasible targets, likely impact and costs for the 2015–2019 national strategic HIV/AIDS plan (NSP).

Methods

The HIV epidemic and response was modelled in the Spectrum/Goals/Resource Needs dynamical simulation model, separately for North/Center/South regions, fitted to antenatal clinic surveillance data, household and key risk group surveys, program statistics, and financial records. Intervention targets were defined in collaboration with the National AIDS Council, Ministry of Health, technical partners and implementing NGOs, considering existing commitments.

Results

Implementing the NSP to meet existing coverage targets would reduce annual new infections among all ages from 105,000 in 2014 to 78,000 in 2019, and reduce annual HIV/AIDS-related deaths from 80,000 to 56,000. Additional scale-up of prevention interventions targeting high-risk groups, with improved patient retention on ART, could further reduce burden to 65,000 new infections and 51,000 HIV-related deaths in 2019. Program cost would increase from US$ 273 million in 2014, to US$ 433 million in 2019 for ‘Current targets’, or US$ 495 million in 2019 for ‘Accelerated scale-up’. The ‘Accelerated scale-up’ would lower cost per infection averted, due to an enhanced focus on behavioural prevention for high-risk groups. Cost and mortality impact are driven by ART, which accounts for 53% of resource needs in 2019. Infections averted are driven by scale-up of interventions targeting sex work (North, rising epidemic) and voluntary male circumcision (Center & South, generalized epidemics).

Conclusion

The NSP could aim to reduce annual new HIV infections and deaths by 2019 by 30% and 40%, respectively, from 2014 levels. Achieving incidence and mortality reductions corresponding to UNAIDS’ ‘Fast track’ targets will require increased ART coverage and additional behavioural prevention targeting key risk groups.     

The Basic Reproduction Number for Cellular SIR Networks

The basic reproduction number \(R_0\) is the average number of new infections produced by a typical infective individual in the early stage of an infectious disease, following the introduction of few infective individuals in a completely susceptible population. If \(R_0<1\) , then the disease dies, whereas for \(R_0>1\) the infection can invade the host population and persist. This threshold quantity is well studied for SIR compartmental or mean field models based on ordinary differential equations, and a general method for its computation has been proposed by van den Driessche and Watmough. We concentrate here on SIR epidemiological models that take into account the contact network N underlying the transmission of the disease. In this context, it is generally admitted that \(R_{0}\) can be approximated by the average number \(R_{2,3}\) of infective individuals of generation three produced by an infective of generation two. We give here a simple analytic formula of \(R_{2,3}\) for SIR cellular networks. Simulations on two-dimensional cellular networks with von Neumann and Moore neighborhoods show that \(R_{2,3}\) can be used to capture a threshold phenomenon related the dynamics of SIR cellular network and confirm the good quality of the simple approach proposed recently by Aparicio and Pascual for the particular case of Moore neighborhood.     

Stability of differential susceptibility and infectivity epidemic models

We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio R₀ ￡ 1{\mathcal{R}_0 \leq 1} and the existence and uniqueness of an endemic equilibrium when ${\mathcal{R}_0 >1 }${\mathcal{R}_0 >1 } . We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when ${\mathcal{R}_0 >1 }${\mathcal{R}_0 >1 } . Our results encompass and generalize those of Hyman and Li (J Math Biol 50:626–644, 2005; Math Biosci Eng 3:89–100, 2006).     

Modeling HIV Vaccines in Brazil: Assessing the Impact of a Future HIV Vaccine on Reducing New Infections,Mortality and Number of People Receiving ARV

Background

The AIDS epidemic in Brazil remains concentrated in populations with high vulnerability to HIV infection, and the development of an HIV vaccine could make an important contribution to prevention. This study modeled the HIV epidemic and estimated the potential impact of an HIV vaccine on the number of new infections, deaths due to AIDS and the number of people receiving ARV treatment, under various scenarios.

Methods and Findings

The historical HIV prevalence was modeled using Spectrum and projections were made from 2010 to 2050 to study the impact of an HIV vaccine with 40% to 70% efficacy, and 80% coverage of adult population, specific groups such as MSM, IDU, commercial sex workers and their partners, and 15 year olds. The possibility of disinhibition after vaccination, neglecting medium- and high-risk groups, and a disease-modifying vaccine were also considered. The number of new infections and deaths were reduced by 73% and 30%, respectively, by 2050, when 80% of adult population aged 15–49 was vaccinated with a 40% efficacy vaccine. Vaccinating medium- and high-risk groups reduced new infections by 52% and deaths by 21%. A vaccine with 70% efficacy produced a great decline in new infections and deaths. Neglecting medium- and high-risk population groups as well as disinhibition of vaccinated population reduced the impact or even increased the number of new infections. Disease-modifying vaccine also contributed to reducing AIDS deaths, the need for ART and new HIV infections.

Conclusions

Even in a country with a concentrated epidemic and high levels of ARV coverage, such as Brazil, moderate efficacy vaccines as part of a comprehensive package of treatment and prevention could have a major impact on preventing new HIV infections and AIDS deaths, as well as reducing the number of people on ARV. Targeted vaccination strategies may be highly effective and cost-beneficial.     

Global analysis of an SAIS model

This paper is concerned with global analysis of an SAIS epidemiological model in a population of varying size introduced by Busenberg and van den Driessche. In this model the population is divided into three subgroups of susceptible, asymptomatic and infective individuals. It has been shown that this system has no periodic solutions and all its trajectories tend to the equilibria of the system. We use the Poincaré Index theorem to determine the number of the equilibria and their stability properties. We have shown that bistability occurs for suitable values of parameters and found a set of examples of all possible dynamics of the system.     

Trends in High-Risk Sexual Behaviors among General Population Groups in China: A Systematic Review

Background

The objective of this review was to investigate whether Chinese population groups that do not belong to classical high risk groups show an increasing trend of engaging in high-risk sexual behaviors.

Methods

We systematically searched the English and Chinese literature on sexual risk behaviors published between January 1980 and March 2012 in PubMed and the China National Knowledge Infrastructure (CNKI). We included observational studies that focused on population groups other than commercial sex workers (CSWs) and their clients, and men who have sex with men (MSM) and quantitatively reported one of the following indicators of recent high-risk sexual behavior: premarital sex, commercial sex, multiple sex partners, condom use or sexually transmitted infections (STIs). We used generalized linear mixed model to examine the time trend in engaging in high-risk sexual behaviors.

Results

We included 174 observational studies involving 932,931 participants: 55 studies reported on floating populations, 73 on college students and 46 on other groups (i.e. out-of-school youth, rural residents, and subjects from gynecological or obstetric clinics and premarital check-up centers). From the generalized linear mixed model, no significant trends in engaging in high-risk sexual behaviors were identified in the three population groups.

Discussion

Sexual risk behaviors among certain general population groups have not increased substantially. These groups are therefore unlikely to incite a STI/HIV epidemic among the general Chinese population. Because the studied population groups are not necessarily representative of the general population, the outcomes found may not reflect those of the general population.     

Periodic orbits arising from Hopf bifurcations in a Volterra prey-predator model

 In this paper we derive a formula which enables the stability of periodic solutions to a Volterra integro-differential system to be determined. This system which has been studied by Cushing [1], models a predator-prey interaction with distributed delays. The results are obtained by using the algorithm developed by Kazarinoff, Wan and van den Driessche [2] based on the centre manifold formulas of Hassard and Wan [3]. We discuss an example of the formula for the case of weak kernels and show that under certain conditions stable periodic solutions arising from Hopf bifurcations at different critical values of the parameters can exist together. Received 30 December 1994; received in revised form 12 December 1995     

Modelling the social dynamics of a sex industry: Its implications for spread of HIV/AIDS

A theoretical model is proposed for a community which has the structure of two classes (direct and indirect) of commercial sex workers (CSW), and two classes of sexually active male customers with different levels of sexual activity. The direct CSW’s work in brothels while the indirect CSW’s are based in commercial establishments such as bars, cafes, and massage parlours where sex can be bought on request and conducted elsewhere. Behaviour change and the resulting change of activity class occurs between the two classes of CSW’s and two classes of males under the setting of the proliferation of human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome epidemic and the subsequent intervention programmes. In recently years, this phenomenon has been observed in several countries in Asia. Given the lower levels of condom use and higher HIV prevalence of the indirect CSW’s, ascertaining the impact of this change in the structure of the sex industry on the spread of HIV is the main focus of this paper. The complete analysis of the disease-free model is given. For the full model, local analysis will be performed for the case of preferred mixing without activity class change, as well as the case with activity class change and restricted mixing. The basic reproduction number for the spread of epidemic will be derived for each case. Results of biological significance include: (i) the change of behaviour by the CSW’s has a more direct effect on the spread of HIV than that of the male customers; (ii) the basic reproduction number is obtained by considering all possible infection cycles of the heterosexual transmission of HIV which indicates the importance of understanding the sexual networking in heterosexual transmission of HIV; (iii) the social dynamics of the sex industry is not just a simple ’supply and demand’ mechanism driven by the demand of the customers, hence highlighting the need for further understanding of the changing structure of the sex industry. The main points of this work will be illustrated with numerical examples using the HIV data of Thailand.     

Prevalence of Type 2 Diabetes among High-Risk Adults in Shanghai from 2002 to 2012

Objective

The objective of this study was to evaluate the trend and prevalence of prediabetes and diabetes among high-risk adults in Shanghai from 2002 to 2012.

Methods

From 2002 to 2012, 10043 subjects with known risk factors for diabetes participated in the diabetes-screening project at the Shanghai Sixth People’s Hospital of Shanghai Jiao Tong University. All participants were asked to complete a nurse-administered standard questionnaire concerning age, sex, smoking status, and personal and family histories of diabetes, cardiovascular disease, stroke, hypertension and other diseases. The participants’ body mass index scores, blood pressures and blood glucose levels at 0, 30, 60, 120 and 180 min were measured in response to a 75 g oral glucose tolerance test.

Results

The overall prevalence of diabetes increased from 27.93% to 34.78% between 2002 and 2012 in high-risk subjects. The study also showed that the prevalence increased much faster in male compared to female subjects. Specifically, an increased rate was seen in middle-aged men, with no change observed in middle-aged females over the eleven-year period.

Conclusion

This study showed that sex, age, parental diabetic history, and being overweight were associated with an increased risk for diabetes in high-risk people. Therefore, as prediabetes and diabetes are highly prevalent in people with multiple diabetes risk factors in Shanghai, screening programs targeting these individuals may be beneficial.