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Modeling the endocrine control of vitellogenin production in female rainbow trout
Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIVepidemic including treatment
1.  Department of Natural Sciences and Mathematics, Richard Stockton College of New Jersey, 101 Vera King Farris Drive, Galloway, NJ 082059441, United States, United States 
References:
[1] 
D. J. Ahlgren, M. K. Gorny and A. C. Stein, Modelbased optimization of infectivity parameters: A study of the early epidemic in San Francisco,, J. Acqr. Immune. Defic. Syndr., 3 (1990), 631. 
[2] 
H. de Arazoza and R. Lounes, A nonlinear model for a sexually transmitted disease with contact tracing,, IMA Journ of Math. Appl. in Medicine and Biology, 19 (2002), 221. 
[3] 
R. B. Bapat and T. E. S. Raghavan, Nonnegative Matrices and Applications,, Cambridge University Press, (1997). doi: 10.1017/CBO9780511529979. 
[4] 
F. Brauer, Some simple epidemic models,, Math Biosci and Engineering, 3 (2006), 1. 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. 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, 19781985,, MMWR, 34 (1985), 573. 
[8] 
J. W. Curran, et al., The epidemiology of AIDS: Current status and future prospects,, Science, 229 (1985), 1352. doi: 10.1126/science.2994217. 
[9] 
C. F. Gilks, S. Crowley and R. Ekpini, et. al., The WHO publichealth approach to antiretroviral treatment against HIV in resourcelimited settings,, Lancet, 368 (2006), 505. doi: 10.1016/S01406736(06)691587. 
[10] 
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmenatl models of disease transmission,, Math Biosci, 180 (2002), 29. doi: 10.1016/S00255564(02)001086. 
[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. doi: 10.1016/S01406736(08)616979. 
[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, (1992). doi: 10.1007/9783642514777. 
[14] 
H. W. Hethcote and J. W. Van Ark, Modeling HIV Transmission and AIDS in the United States,, SpringerVerlag, (1992). doi: 10.1007/9783642514777. 
[15] 
H. W. Jaffe, et al., The acquired immunodeficiency syndrome in a cohort of homosexual men: a sixyear followup study,, Ann. Intern. Med., 103 (1985), 210. doi: 10.7326/000348191032210. 
[16] 
A. Lajmanovich and J. A. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population,, Math Biosci, 28 (1976), 221. doi: 10.1016/00255564(76)901255. 
[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. doi: 10.1016/00255564(80)900693. 
[19] 
NIH, Guidelines for the Use of Antiretroviral Agents in HIV1Infected Adults and Adolescents,, , (2012). 
[20] 
S. M. Osnaga, On rank one matrices and invariant subspaces,, Balkan J. of Geometry and Its Applications, 10 (2005), 145. 
[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 HIVAIDS in Cuba during the period 19862000,, Math Biosci and Engineering, 3 (2006), 545. doi: 10.3934/mbe.2006.3.545. 
[23] 
B. L. Rapatski, F. Suppe and J. A. Yorke, HIV epidemics driven by late diseasestage transmission,, JAIDS, 38 (2005), 241. 
[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 AIDSfree HIV1infected patients: A collaborative analysis of 18 HIV cohort studies,, Lancet, 373 (2009), 1352. 
[26] 
C. K. Yang and F. Brauer, Calculation of $R_0$ for ageofinfection models,, Math Biosci and Engineering, 5 (2008), 585. 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. doi: 10.1001/jama.1987.03390030051019. 
show all references
References:
[1] 
D. J. Ahlgren, M. K. Gorny and A. C. Stein, Modelbased optimization of infectivity parameters: A study of the early epidemic in San Francisco,, J. Acqr. Immune. Defic. Syndr., 3 (1990), 631. 
[2] 
H. de Arazoza and R. Lounes, A nonlinear model for a sexually transmitted disease with contact tracing,, IMA Journ of Math. Appl. in Medicine and Biology, 19 (2002), 221. 
[3] 
R. B. Bapat and T. E. S. Raghavan, Nonnegative Matrices and Applications,, Cambridge University Press, (1997). doi: 10.1017/CBO9780511529979. 
[4] 
F. Brauer, Some simple epidemic models,, Math Biosci and Engineering, 3 (2006), 1. 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. 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, 19781985,, MMWR, 34 (1985), 573. 
[8] 
J. W. Curran, et al., The epidemiology of AIDS: Current status and future prospects,, Science, 229 (1985), 1352. doi: 10.1126/science.2994217. 
[9] 
C. F. Gilks, S. Crowley and R. Ekpini, et. al., The WHO publichealth approach to antiretroviral treatment against HIV in resourcelimited settings,, Lancet, 368 (2006), 505. doi: 10.1016/S01406736(06)691587. 
[10] 
P. van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmenatl models of disease transmission,, Math Biosci, 180 (2002), 29. doi: 10.1016/S00255564(02)001086. 
[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. doi: 10.1016/S01406736(08)616979. 
[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, (1992). doi: 10.1007/9783642514777. 
[14] 
H. W. Hethcote and J. W. Van Ark, Modeling HIV Transmission and AIDS in the United States,, SpringerVerlag, (1992). doi: 10.1007/9783642514777. 
[15] 
H. W. Jaffe, et al., The acquired immunodeficiency syndrome in a cohort of homosexual men: a sixyear followup study,, Ann. Intern. Med., 103 (1985), 210. doi: 10.7326/000348191032210. 
[16] 
A. Lajmanovich and J. A. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population,, Math Biosci, 28 (1976), 221. doi: 10.1016/00255564(76)901255. 
[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. doi: 10.1016/00255564(80)900693. 
[19] 
NIH, Guidelines for the Use of Antiretroviral Agents in HIV1Infected Adults and Adolescents,, , (2012). 
[20] 
S. M. Osnaga, On rank one matrices and invariant subspaces,, Balkan J. of Geometry and Its Applications, 10 (2005), 145. 
[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 HIVAIDS in Cuba during the period 19862000,, Math Biosci and Engineering, 3 (2006), 545. doi: 10.3934/mbe.2006.3.545. 
[23] 
B. L. Rapatski, F. Suppe and J. A. Yorke, HIV epidemics driven by late diseasestage transmission,, JAIDS, 38 (2005), 241. 
[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 AIDSfree HIV1infected patients: A collaborative analysis of 18 HIV cohort studies,, Lancet, 373 (2009), 1352. 
[26] 
C. K. Yang and F. Brauer, Calculation of $R_0$ for ageofinfection models,, Math Biosci and Engineering, 5 (2008), 585. 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. doi: 10.1001/jama.1987.03390030051019. 
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