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

Rapatski, B.; Tolosa, J.

Mathematical Biosciences and Engineering Mbe 11(3): 599-619

2014


ISSN/ISBN: 1551-0018
PMID: 24506553
Accession: 054412365

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Abstract
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.