Mathematical Biosciences and Engineering, 2014, 11(3): 599-619. doi: 10.3934/mbe.2014.11.599.

Primary: 92D30, 34A34, 34D23; Secondary: 93D05.

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

1. Department of Natural Sciences and Mathematics, Richard Stockton College of New Jersey, 101 Vera King Farris Drive, Galloway, NJ 08205-9441

We investigate two HIV/AIDS epidemic models.The first model represents the early San Franciscomen having sex with men (MSM) epidemic.We use data from the San Francisco City Clinic Cohort Study (SFCCC), documentingthe onset of HIV in San Francisco (1978-1984).The second model is a ``what-if'' scenario model includingtesting and treatment in the SFCCC epidemic.We use compartmental, population-level models,described by systems ofordinary differential equations.We find the basic reproductive number $R_0$ for each system,and we prove that if $R_0<1 the="" system="" has="" only="" the="" disease-free="" equilibrium="" dfe="" which="" is="" locally="" and="" globally="" stable="" whereas="" if="" r_0="">1$, the DFE is unstable.In addition, when $R_0>1$, 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.
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Keywords mathematical model; Lyapunov function.; reproduction number; stability; Human Immunodeficiency Virus (HIV)

Citation: Brandy Rapatski, Juan Tolosa. Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment. Mathematical Biosciences and Engineering, 2014, 11(3): 599-619. doi: 10.3934/mbe.2014.11.599

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This article has been cited by

  • 1. Brandy Rapatski, Juan Tolosa, The San Francisco MSM Epidemic: A Retrospective Analysis, Mathematics, 2015, 3, 4, 1083, 10.3390/math3041083

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