Influence of concurrency, partner choice, and viral suppression on racial disparity in the prevalence of HIV infected women.

In 1992, Watts and May introduced a simple dynamical systems model of the spread of HIV based on disease transmission per partnership including the length of partnership duration. This model allowed for the treatment of concurrent partnerships, although it was hampered by the assumption of an important latent phase which generated a non-autonomous system. Subsequent models including concurrency have been based on networks, Monte Carlo, and stochastic simulations which lose a qualitative understanding of the effects of concurrency. We present a new autonomous deterministic model of the effect of concurrent sexual partnerships that allows for an analytical study of disease transmission. We incorporate the effect of concurrency through the newly derived force of infection term in a mathematical model of the transmission of HIV through sexual contact in a population stratified by sexual behavior and race/ethnicity. The model also includes variations in population mixing (partner choice) and non-uniform Highly Active Anti-Retroviral Treatment (HAART) leading to viral suppression. We use this mathematical model to understand the non-uniform spread of HIV in women who were infected through heterosexual contact. In addition, an analytical study shows the importance of continued condom use in virally suppressed MSM. Numerical simulations of the reproduction number as a function of concurrency, viral suppression level, and mixing show a reservoir of disease present in both heterosexual and MSM populations. Statistical analysis of parameter values show that viral suppression level, mixing and progression to AIDS without viral suppression have a strong correlation (either positive or negative) with the number of HIV positive women. Concurrency and assortative mixing are shown to be essential to reproduce infection levels in women, as reported by 2010 data from the Center for Disease Control (CDC).