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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 3: 599-619. doi: 10.3934/mbe.2014.11.599
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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
  • Received: 01 August 2012 Accepted: 29 June 2018 Published: 01 January 2014

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

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    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.

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

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  • 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.


    [1] J. Acqr. Immune. Defic. Syndr., 3 (1990), 631-643.
    [2] IMA Journ of Math. Appl. in Medicine and Biology, 19 (2002), 221-234.
    [3] Cambridge University Press, New York, 1997.
    [4] Math Biosci and Engineering, 3 (2006), 1-15.
    [5] J. Biological Dynamics, 3 (2009), 324-330.
    [6] The Washington Post, 2011.
    [7] MMWR, 34 (1985), 573-575.
    [8] Science, 229 (1985), 1352-1357.
    [9] Lancet, 368 (2006), 505-510.
    [10] Math Biosci, 180 (2002), 29-48.
    [11] Lancet, 373 (2009), 48-57.
    [12] Baltimore, 1973.
    [13] Berlin: New York, Springer-Verlag, 1992.
    [14] Springer-Verlag, 1992.
    [15] Ann. Intern. Med., 103 (1985), 210-214.
    [16] Math Biosci, 28 (1976), 221-236.
    [17] The Washington Post, 2011.
    [18] Math Biosci, 52 (1980), 227-240.
    [19] http://aidsinfo.nih.gov/contentfiles/lvguidelines/AdultandAdolescentGL.pdf (2012).
    [20] Balkan J. of Geometry and Its Applications, 10 (2005), 145-148.
    [21] The Washington Post, 2011.
    [22] Math Biosci and Engineering, 3 (2006), 545-556.
    [23] JAIDS, 38 (2005), 241-253.
    [24] paper submitted for publication.
    [25] Lancet, 373 (2009), 1352-1363.
    [26] Math Biosci and Engineering, 5 (2008), 585-599.
    [27] JAMA, 257 (1987), 321-325.

  • This article has been cited by:

    1. Brandy Rapatski, Juan Tolosa, The San Francisco MSM Epidemic: A Retrospective Analysis, 2015, 3, 2227-7390, 1083, 10.3390/math3041083
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