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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, United States, United States |
References:
[1] |
D. J. Ahlgren, M. K. Gorny and A. C. Stein, Model-based optimization of infectivity parameters: A study of the early epidemic in San Francisco, J. Acqr. Immune. Defic. Syndr., 3 (1990), 631-643. |
[2] |
H. de Arazoza and R. Lounes, A non-linear model for a sexually transmitted disease with contact tracing, IMA Journ of Math. Appl. in Medicine and Biology, 19 (2002), 221-234. |
[3] |
R. B. Bapat and T. E. S. Raghavan, Non-negative Matrices and Applications, Cambridge University Press, New York, 1997.
doi: 10.1017/CBO9780511529979. |
[4] |
F. Brauer, Some simple epidemic models, Math Biosci and Engineering, 3 (2006), 1-15.
doi: 10.3934/mbe.2006.3.1. |
[5] |
F. Brauer and J. Watmough, Age of infection epidemic models with heterogeneous mixing, J. Biological Dynamics, 3 (2009), 324-330.
doi: 10.1080/17513750802415822. |
[6] |
D. Brown, HIV Drugs Sharply Cut Risk of Transmission, Study Finds, The Washington Post, 2011. |
[7] |
CDC, Update: Acquired immunodeficiency syndrome in the San Francisco cohort study, 1978-1985, MMWR, 34 (1985), 573-575. |
[8] |
J. W. Curran, et al., The epidemiology of AIDS: Current status and future prospects, Science, 229 (1985), 1352-1357.
doi: 10.1126/science.2994217. |
[9] |
C. F. Gilks, S. Crowley and R. Ekpini, et. al., The WHO public-health approach to antiretroviral treatment against HIV in resource-limited settings, Lancet, 368 (2006), 505-510.
doi: 10.1016/S0140-6736(06)69158-7. |
[10] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmenatl models of disease transmission, Math Biosci, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[11] |
R. M. Granich, C. F. Gilks, C. Dye and K. M. De Cock and B. G. Williams, Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: A mathematical model, Lancet, 373 (2009), 48-57.
doi: 10.1016/S0140-6736(08)61697-9. |
[12] |
P. Hartman, Ordinary Differential Equations, Baltimore, 1973. |
[13] |
H. W. Hethcote and J. W. Van Ark, Modeling HIV Transmission and AIDS in the United States, Berlin: New York, Springer-Verlag, 1992.
doi: 10.1007/978-3-642-51477-7. |
[14] |
H. W. Hethcote and J. W. Van Ark, Modeling HIV Transmission and AIDS in the United States, Springer-Verlag, 1992.
doi: 10.1007/978-3-642-51477-7. |
[15] |
H. W. Jaffe, et al., The acquired immunodeficiency syndrome in a cohort of homosexual men: a six-year follow-up study, Ann. Intern. Med., 103 (1985), 210-214.
doi: 10.7326/0003-4819-103-2-210. |
[16] |
A. Lajmanovich and J. A. Yorke, A deterministic model for gonorrhea in a non-homogeneous population, Math Biosci, 28 (1976), 221-236.
doi: 10.1016/0025-5564(76)90125-5. |
[17] |
B. McKay, Scientists See Breakthrough in the Global AIDS Battle, The Washington Post, 2011. |
[18] |
A. Nold, Heterogeinity in disease transmission modeling, Math Biosci, 52 (1980), 227-240.
doi: 10.1016/0025-5564(80)90069-3. |
[19] |
NIH, Guidelines for the Use of Antiretroviral Agents in HIV-1-Infected Adults and Adolescents, http://aidsinfo.nih.gov/contentfiles/lvguidelines/AdultandAdolescentGL.pdf (2012). |
[20] |
S. M. Osnaga, On rank one matrices and invariant subspaces, Balkan J. of Geometry and Its Applications, 10 (2005), 145-148. |
[21] |
J. Price, Study: Early HIV Treatment Slows Spread of Disease, Lexington Herald Chapel Hill, The Washington Post, 2011. |
[22] |
B. L. Rapatski, P. Klepak, S. Dueck, M. Liu, and L. I. Weiss, Mathematical epidemiology of HIV-AIDS in Cuba during the period 1986-2000, Math Biosci and Engineering, 3 (2006), 545-556.
doi: 10.3934/mbe.2006.3.545. |
[23] |
B. L. Rapatski, F. Suppe and J. A. Yorke, HIV epidemics driven by late disease-stage transmission, JAIDS, 38 (2005), 241-253. |
[24] |
B. L. Rapatski and J. Tolosa, What would have stopped the San Francisco gay HIV/AIDS epidemic, paper submitted for publication. |
[25] |
J. Sterne, M. May and D. Costagliola, et. al., Timing of initiation of antiretroviral therapy in AIDS-free HIV-1-infected patients: A collaborative analysis of 18 HIV cohort studies, Lancet, 373 (2009), 1352-1363. |
[26] |
C. K. Yang and F. Brauer, Calculation of $R_0$ for age-of-infection models, Math Biosci and Engineering, 5 (2008), 585-599.
doi: 10.3934/mbe.2008.5.585. |
[27] |
W. Winkelstein, D. M. Lyman, N. Padian, R. Grant and M. Samuel, J. A. Wiley, R. E. Anderson, W. Lang, J. Riggs and J. A. Levy, Sexual practices and risk of infection by the human immunodeficiency virus: the San Francisco men's health study, JAMA, 257 (1987), 321-325.
doi: 10.1001/jama.1987.03390030051019. |
show all references
References:
[1] |
D. J. Ahlgren, M. K. Gorny and A. C. Stein, Model-based optimization of infectivity parameters: A study of the early epidemic in San Francisco, J. Acqr. Immune. Defic. Syndr., 3 (1990), 631-643. |
[2] |
H. de Arazoza and R. Lounes, A non-linear model for a sexually transmitted disease with contact tracing, IMA Journ of Math. Appl. in Medicine and Biology, 19 (2002), 221-234. |
[3] |
R. B. Bapat and T. E. S. Raghavan, Non-negative Matrices and Applications, Cambridge University Press, New York, 1997.
doi: 10.1017/CBO9780511529979. |
[4] |
F. Brauer, Some simple epidemic models, Math Biosci and Engineering, 3 (2006), 1-15.
doi: 10.3934/mbe.2006.3.1. |
[5] |
F. Brauer and J. Watmough, Age of infection epidemic models with heterogeneous mixing, J. Biological Dynamics, 3 (2009), 324-330.
doi: 10.1080/17513750802415822. |
[6] |
D. Brown, HIV Drugs Sharply Cut Risk of Transmission, Study Finds, The Washington Post, 2011. |
[7] |
CDC, Update: Acquired immunodeficiency syndrome in the San Francisco cohort study, 1978-1985, MMWR, 34 (1985), 573-575. |
[8] |
J. W. Curran, et al., The epidemiology of AIDS: Current status and future prospects, Science, 229 (1985), 1352-1357.
doi: 10.1126/science.2994217. |
[9] |
C. F. Gilks, S. Crowley and R. Ekpini, et. al., The WHO public-health approach to antiretroviral treatment against HIV in resource-limited settings, Lancet, 368 (2006), 505-510.
doi: 10.1016/S0140-6736(06)69158-7. |
[10] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmenatl models of disease transmission, Math Biosci, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[11] |
R. M. Granich, C. F. Gilks, C. Dye and K. M. De Cock and B. G. Williams, Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission: A mathematical model, Lancet, 373 (2009), 48-57.
doi: 10.1016/S0140-6736(08)61697-9. |
[12] |
P. Hartman, Ordinary Differential Equations, Baltimore, 1973. |
[13] |
H. W. Hethcote and J. W. Van Ark, Modeling HIV Transmission and AIDS in the United States, Berlin: New York, Springer-Verlag, 1992.
doi: 10.1007/978-3-642-51477-7. |
[14] |
H. W. Hethcote and J. W. Van Ark, Modeling HIV Transmission and AIDS in the United States, Springer-Verlag, 1992.
doi: 10.1007/978-3-642-51477-7. |
[15] |
H. W. Jaffe, et al., The acquired immunodeficiency syndrome in a cohort of homosexual men: a six-year follow-up study, Ann. Intern. Med., 103 (1985), 210-214.
doi: 10.7326/0003-4819-103-2-210. |
[16] |
A. Lajmanovich and J. A. Yorke, A deterministic model for gonorrhea in a non-homogeneous population, Math Biosci, 28 (1976), 221-236.
doi: 10.1016/0025-5564(76)90125-5. |
[17] |
B. McKay, Scientists See Breakthrough in the Global AIDS Battle, The Washington Post, 2011. |
[18] |
A. Nold, Heterogeinity in disease transmission modeling, Math Biosci, 52 (1980), 227-240.
doi: 10.1016/0025-5564(80)90069-3. |
[19] |
NIH, Guidelines for the Use of Antiretroviral Agents in HIV-1-Infected Adults and Adolescents, http://aidsinfo.nih.gov/contentfiles/lvguidelines/AdultandAdolescentGL.pdf (2012). |
[20] |
S. M. Osnaga, On rank one matrices and invariant subspaces, Balkan J. of Geometry and Its Applications, 10 (2005), 145-148. |
[21] |
J. Price, Study: Early HIV Treatment Slows Spread of Disease, Lexington Herald Chapel Hill, The Washington Post, 2011. |
[22] |
B. L. Rapatski, P. Klepak, S. Dueck, M. Liu, and L. I. Weiss, Mathematical epidemiology of HIV-AIDS in Cuba during the period 1986-2000, Math Biosci and Engineering, 3 (2006), 545-556.
doi: 10.3934/mbe.2006.3.545. |
[23] |
B. L. Rapatski, F. Suppe and J. A. Yorke, HIV epidemics driven by late disease-stage transmission, JAIDS, 38 (2005), 241-253. |
[24] |
B. L. Rapatski and J. Tolosa, What would have stopped the San Francisco gay HIV/AIDS epidemic, paper submitted for publication. |
[25] |
J. Sterne, M. May and D. Costagliola, et. al., Timing of initiation of antiretroviral therapy in AIDS-free HIV-1-infected patients: A collaborative analysis of 18 HIV cohort studies, Lancet, 373 (2009), 1352-1363. |
[26] |
C. K. Yang and F. Brauer, Calculation of $R_0$ for age-of-infection models, Math Biosci and Engineering, 5 (2008), 585-599.
doi: 10.3934/mbe.2008.5.585. |
[27] |
W. Winkelstein, D. M. Lyman, N. Padian, R. Grant and M. Samuel, J. A. Wiley, R. E. Anderson, W. Lang, J. Riggs and J. A. Levy, Sexual practices and risk of infection by the human immunodeficiency virus: the San Francisco men's health study, JAMA, 257 (1987), 321-325.
doi: 10.1001/jama.1987.03390030051019. |
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