Abstract
This paper presents a mathematical model of heterogeneous mixing which is designed to explore the effects of partner selection on the transmission patterns of sexually transmitted diseases. The model generates a symmetric matrix of the rate of sexual contacts between individuals categorized into discrete population subgroups. Sexual pairing results from a process with three separate stages: 1) social contact, 2) acceptance as a potential sex partner, and 3) initiation of sex in response to the needs and standards of each partner. This model can define the contact pattern within any single activity group of the structured mixing model presented by Jacquez et al (1989) in this volume. In such a formulation, the rate of new sexual partnership formation is determined by the number of available partners as well as by sexual needs and moral standards and can vary throughout the course of an epidemic. This approach provides a framework for exploring the potential consequences on infectious disease transmission of different sociological factors while at the same time providing a framework for testing specific sociological theory. We present an example of an epidemic in a male homosexual population where all sexual partnerships are short term. The parameters relating the acceptance of one group by another as potential sexual partners vary by the relative sexual activity rates of individuals and by their relative preference for oral or anal sex. Per sex act transmission probabilities for anal sex were made four times as high as oral sex. Proportional mixing results in a corresponding fourfold difference in risks of oral and anal sex. A moderate degree of selective mixing, however, generates a thirty two fold difference in the risk of oral and anal sex during the stage of the epidemic corresponding to that in which epidemiologic studies have been used to assess the relative risks of oral and anal sex.
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References
Chmiel, J.S., R. Detels, R.A. Kaslow, L. VanRaden, M. Kingsley, R. Brookmeyer. (1987).Factors associated with prevalent Human Immunodeficiency Virus (HIV) infection in the multicenter AIDS cohort study. Am J Epidemiol; 126(4): 568–577.
Darrow, W.W., D.F. Echenberg, H.W. Jaffe HW, P. O’Malley, R.H. Byers, J.P. Getchell, J.W. Curran. (1987). Risk factors for Human Immunodeficiency Virus (HIV) infections in homosexual men. Am J Public Health; 77(4): 479–483.
Dietz, K., (1988). On the transmission dynamics of HIV. Math Biosci; 90: 397–414
Dietz, K., K.P. Hadeler. (1988). Epidemiological models for sexually transmitted diseases. J Math Biol 26:1–25.
Fischi, M.A., G.M. Dickinson, G.B. Scott GB, N. Klimas, M.A. Fletcher, W. Parks. (1987). Evaluation of heterosexual partners, children and household contacts of adults with AIDS. JAMA 257:640–4.
Gail, M.H., D. Preston, S. Piantados. (1989) Disease prevention models of voluntary confidential screening for Human Immunodeficiency Virus (HIV) in isolated low risk and high risk populations and in mixed gay/heterosexual populations. Statistics in Medicine; 8:59–81.
Goedert, J.J. (1984). Determinants of retrovirus (HTLV-III) antibody and immunodeficiency conditions in homosexual men. The Lancet, (September 29) 711–715.
Goedert, J.J., R.J. Biggar, D.M. Winn. (1985). Decreased helper T lymphocytes in homosexual men: Sexual Practices. American Journal of Epidemiology; 121(5): 629–36.
Goedert, J.J., R. J. Biggar, M. Melbye, D.L. Mann, S. Wilson, M.H. Gail, R.J. Grossman, R.A. DiGioia, W.C. Sachez, S.H. Weiss, W.A. Blattner. (1987). Effect of T4 count and cofactors on the incidence of AIDS in homosexual men infected with Human Immunodeficiency Virus. JAMA; 257(3): 331–334.
Hethcote, H.W., J.W. Van Ark. (1987). Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs. Math.Biosci. 84:85–118.
Jacquez, J.A. (1985) Compartmental analysis in biology and medicine, Chapter 7, second edition. Ann Arbor: The University of Michigan Press.
Jacquez, J.A., C.P. Simon, J.S. Koopman, L. Sattenspiel, T. Perry. (1988). Modeling and analyzing HIV transmission: the effect of contact patterns. Mathematical Biosciences, 92:119–199.
Jacquez, J.A., J. Koopman, C.P. Simon. (1989). Structured mixing: heterogeneous mixing by the definition of activity groups. A new general method for describing contact patterns with special reference to AIDS. (This volume).
Jeffries, E., B. Willoughby, W.J. Boyko, M.T. Schecter, B. Wiggs, S. Fay, M. O’Shaughnessy. (1985). The Vancouver Lymphadenopathy-AIDS Study: 2. Seroepidemiology of HTLV-m antibody. Can Med Assoc J; 132:1373–1377.
Joseph, J.G., S.B. Montgomery, CA. Emmons, D.G. Ostrow. (1987). Magnitude and determinants of behavioral risk reduction: longitudinal analysis of a cohort at risk for AIDS. Psychology and Health, 1987:73–95.
Kingsley, L.A., R. Kaslow, C.R. Rinaldo, K. Detre, N. Odaka, M. VanRaden, R. Detels, B.F. Polk, J. Chmiel, S.F. Kelsey, D. Ostrow, B. Visscher. (1987). Risk factors for seroconversion to Human Immunodeficiency Virus among male homosexuals. The Lancet (February 14) 345–348.
Koopman, J.S., C.P. Simon, J.A. Jacquez, T.S. Park. (1988). Sexual partner selectiveness effects on homosexual HTV transmission dynamics. Journal of the Acquired Immune Deficiency Syndrome, 1:486–504.
Laumann, E.O., Gagnon JH; Michael, RT (1987). Social and Behavioral Aspects of Health and Fertility-Related Behavior: Technical Proposal submitted in response to National Institute for Child Health and Human Development RFP no. NICHD-DBS-87–13. September 1, 1987. (Available from the Authors).
Longini, I.M., W.S. Clark, R.H. Byers, J.W. Ward, W.W. Darrow, G.F. Lemp, H.A. Hethcote. (1989). Statistical analysis of the stages of HIV infection using a Markov model. Statistics in Medicine 8:(In Press)
Lyman, D., M. Ascher, J.A. Levy. (1986). Minimal risk of transmission of AIDS-Associated retrovirus infection by oral-genital contact (letter). JAMA; 255(13):1703
Melbye, M., R.J. Biggar, P. Ebbesen, M.G. Sarngadharan, S.H. Weiss, R. Gallo R, W.A. Blattner. (1984). Seroepidemiology of HTLV-in antibody in Danish homosexual men: prevalence, transmission, and disease outcome. Br Med J (September 8) 289: 573–575.
Moss, A.R., D. Osmond, P. Bacchetti. (1987). Risk factors for AIDS and HIV seropositivity in homosexual men. American Journal of Epidemiology; 125(6): 1035–1046.
Nicholson, J.K.A., J.S. McDougal, H.W. Jaffe, T.J. Spira, M.S. Kennedy, B.M. Jones, W.W. Darrow, M. Morgan, M Hubbard. (1985). Exposure to Human T-Lymphotropic Virus Type III/Lymphadenopathy-Associated Virus and immunologic abnormalities in asymptomatic homosexual men. Ann Intern Med; 103: 37–42.
Polk, B.F., R. Fox, R. Brookmeyer, S. Kanchanaraksa, R. Kaslow, B. Visscher, C. Rinaldo, J. Phair, (1986). Predictors of the Acquired Immunodeficiency Syndrome developing in a cohort of seropositive homosexual men. N Engl J Med; 316(2): 61 – 66.
Schechter, M.T., W.J. Boyko, B. Douglas, M. Maynard, B. Willoughby, A. McLeod, A. K.J.P. Craib. (1986). Can HTLV-III be transmitted orally? (letter). Lancer, (February 15,1986): 379.
Stevens, C.E., P.E. Taylor, E.A. Zang, J.M. Morrison, E.J. Harley, S.R. Cordoba, C. Bacino, R.C. Ting, A.J. Bodner, M.G. Sarngadharan, R.C. Gallo, P. Rubinstein. (1986). Human T-cell Lymphotropic Virus infection in a cohort of homosexual men in New York City. JAMA; 2556(16): 2167–72.
Winkelstein, W., D.M. Lyman, N. Padian N, R. Grant, M. Samuel, J.A. Wiley, R.E. Anderson, W. Lang, J. Riggs, J. Levy. (1987). Sexual practices and risk of infection by the Human Immunodeficiency Virus; the San Francisco Men’s Health Study. JAMA; 257(3): 321–25.
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Koopman, J.S., Simon, C.P., Jacquez, J.A., Park, T.S. (1989). Selective Contact within Structured Mixing with an Application to HIV Transmission Risk from Oral and Anal Sex. In: Castillo-Chavez, C. (eds) Mathematical and Statistical Approaches to AIDS Epidemiology. Lecture Notes in Biomathematics, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93454-4_16
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DOI: https://doi.org/10.1007/978-3-642-93454-4_16
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