Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment.

We investigate two HIV/AIDS epidemic models. The first model represents the early San Francisco men having sex with men (MSM) epidemic. We use data from the San Francisco City Clinic Cohort Study (SFCCC), documenting the onset of HIV in San Francisco (1978-1984). The second model is a 'what-if' scenario model including testing and treatment in the SFCCC epidemic. We use compartmental, population-level models, described by systems of ordinary differential equations. We find the basic reproductive number R0 for each system, and we prove that if R0<1, the system has only the disease-free equilibrium (DFE) which is locally and globally stable, whereas if R0>1, the DFE is unstable. In addition, when R0>1, both systems have a unique endemic equilibrium (EE). We show that treatment alone would not have stopped the San Francisco MSM epidemic, but would have significantly reduced its impact.

Modeling HIV outbreaks: the male to female prevalence ratio in the core population.

What affects the ratio of infected men to infected women in the core population in a heterosexual HIV epidemic? Hethcote and Yorke [5] introduced the term "core" initially to loosely describe the collection of individuals having the most unprotected sex partners. We study the early epidemic during the exponential growth phase and focus on the core group because most infected people were infected by people in the core. We argue that in the early outbreak phase of an epidemic, there is an identity, which we call the "outbreak equation." It relates three ratios that describe the core men versus the core women, namely, the ratio E of numbers of all core men to all core women, the ratio C of numbers of infected core men to core women, and the ratio M of the infectiousness of a typical core man to that of a typical core woman. Then the relationship between the ratios is E=MC(2) in the early outbreak phase. We investigate two very different scenarios, one in which there are two times as many core men as core women (E=2) and the other in which core men equal core women (E=1). In the first case, the HIV epidemic grows at a much faster rate. We conclude that if the female core group was larger, that is, if more women in the total population were promiscuous (or if fewer men were promiscuous) then the HIV epidemic would grow more slowly.

Reconciling different infectivity estimates for HIV-1.

In our article, "HIV-1 Epidemics Driven by Late Stage Disease," we conclude that the probability of transmission of HIV through promiscuous or casual sexual contacts is significantly higher in the third or symptomatic stage of the disease. Our results differ greatly from those of the current literature. The primary stage or first stage has been reported to be the most infectious based on an article by Jacquez et al. More recently, the Wawer et al study of monogamous heterosexual couples in Rakai, Uganda found that the transmission of HIV was most likely to occur in the first 5 months after infection. We describe how the findings of the Wawer et al study might be compatible with our results. We also respond to a response by Koopman and Simon, who seem to criticize their own paper severely and choose not to defend it against our remarks.

HIV epidemics driven by late disease stage transmission.

How infectious a person is when infected with HIV depends on what stage of the disease the person is in. We use 3 stages, which we call primary, asymptomatic, and symptomatic. It is important to have a systematic method for computing all 3 infectivities so that the measurements are comparable. Using robust modeling, we provide high-resolution estimates of semen infectivity by HIV disease stage. We find that the infectivity of the symptomatic stage is far higher, hence more potent, than the values that prior studies have used when modeling HIV transmission dynamics. The stage infectivity rates for semen are 0.024, 0.002, and 0.299 for the primary, asymptomatic, and symptomatic stages, respectively. Implications of our infectivity estimates and modeling for understanding heterosexual epidemics such as that in sub-Saharan African are explored.