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.