A state space model for the HIV epidemic in homosexual populations and some applications

Mathematical models for the study of HIV spread and control amongst men who have sex with men

For a quarter of century, mathematical models have been used to study the spread and control of HIV amongst men who have sex with men (MSM). We searched MEDLINE and EMBASE databases up to the end of 2010 and reviewed this literature to summarise the methodologies used, key model developments, and the recommended strategies for HIV control amongst MSM. Of 742 studies identified, 127 studies met the inclusion criteria. Most studies employed deterministic modelling methods (80%). Over time we saw an increase in model complexity regarding antiretroviral therapy (ART), and a corresponding decrease in complexity regarding sexual behaviours. Formal estimation of model parameters was carried out in only a small proportion of the studies (22%) while model validation was considered by an even smaller proportion (17%), somewhat reducing confidence in the findings from the studies. Nonetheless, a number of common conclusions emerged, including (1) identification of the importance of assumptions regarding changes in infectivity and sexual contact rates on the impact of ART on HIV incidence, that subsequently led to empirical studies to gather these data, and (2) recommendation that multiple strategies would be required for effective HIV control amongst MSM. The role of mathematical models in studying epidemics is clear, and the lack of formal inference and validation highlights the need for further developments in this area. Improved methodologies for parameter estimation and systematic sensitivity analysis will help generate predictions that more fully express uncertainty, allowing better informed decision making in public health.

A sex-role-preference model for HIV transmission among men who have sex with men in China

Background

Men who have sex with men (MSM) are much more likely to be infected with HIV than the general population. China has a sizable population of MSM, including gay, bisexual men, money boys and some rural workers. So reducing HIV infection in this population is an important component of the national HIV/AIDS prevention and control program.

Methods

We develop a mathematical model using a sex-role-preference framework to predict HIV infection in the MSM population and to evaluate different intervention strategies.

Results

An analytic formula for the basic reproduction ratio R₀ was obtained; this yields R₀ = 3.9296 in the current situation, so HIV will spread very fast in the MSM population if no intervention measure is implemented in a timely fashion. The persistence of HIV infection and the existence of disease equilibrium (or equilibria) are also shown. We utilized our model to simulate possible outcomes of antiretroviral therapy and vaccination for the MSM population. We compared the effects of these intervention measures under different assumptions about MSM behaviour. We also found that R₀ is a decreasing function of the death rate of HIV-infected individuals, following a power law at least asymptotically.

Conclusion

HIV will spread very fast in the MSM population unless intervention measures are implemented urgently. Antiretroviral therapy can have substantial impact on the reduction of HIV among the MSM population, even if disinhibition is considered. The effect of protected sexual behaviour on controlling the epidemic in the MSM population largely depends on the sex-ratio preference of different sub-populations.

Stochastic models for the spread of HIV in a mobile heterosexual population

An important factor in the dynamic transmission of HIV is the mobility of the population. We formulate various stochastic models for the spread of HIV in a heterosexual mobile population, under the assumptions of constant and varying population sizes. We also derive deterministic and diffusion analogues for these models, using a convenient rescaling technique, and analyze their stability conditions and equilibrium behavior. We illustrate the dynamic behavior of the models and their approximations via a range of numerical experiments.

Estimation of HIV infection and incubation via state space models

By using the state space model (Kalman filter model) of the HIV epidemic, in this paper we have developed a general Bayesian procedure to estimate simultaneously the HIV infection distribution, the HIV incubation distribution, the numbers of susceptible people, infective people and AIDS cases. The basic approach is to use the Gibbs sampling method combined with the weighted bootstrap method. We have applied this method to the San Francisco AIDS incidence data from January 1981 to December 1992. The results show clearly that both the probability density function of the HIV infection and the probability density function of the HIV incubation are curves with two peaks. The results of the HIV infection distribution are clearly consistent with the finding by Tan et al. [W.Y. Tan, S.C. Tang, S.R. Lee, Estimation of HIV seroconversion and effects of age in San Francisco homosexual populations, J. Appl. Stat. 25 (1998) 85]. The results of HIV incubation distribution seem to confirm the staged model used by Satten and Longini [G. Satten, I. Longini, Markov chain with measurement error: estimating the 'true' course of marker of the progression of human immunodeficiency virus disease, Appl. Stat. 45 (1996) 275].