Abstract
The model formulated for transmission of HIV (the AIDS virus) and the subsequent progression to AIDS is a system of nonlinear differential equations. They describe the infection process by interactions within and between risk groups such as homosexual men, bisexual men, female prostitutes, intravenous drug abusers and heterosexually active men and women. The progression to AIDS after infection is modeled by a sequence of stages. A modification of this model is being used to study the transmission of HIV infection and the incidence of AIDS in risk groups in the United States.
Supported by Contract 200-87-0515 from the Centers for Disease Control.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson R.M., May R.M., and McLean A.R. (1988). Possible demographic consequences of AIDS in developing countries, Nature 332, 228–234.
Anderson R.M., Medley G.F., May R.M. and Johnson A.M. (1986). A preliminary study of the transmission dynamics of the H.I.V., the causative agent of AIDS, IMA J Math Appl in Med and Biol 3, 229–263.
Bailey N.T.J. and Duppenthaler J. (1985). Sensitivity analysis in the modeling of infectious disease dynamics, J Math Biology 10, 113–131.
Bongaarts J. (1987). A model of the spread of HIV infection and the demographic impact of AIDS, preprint, 24 pages.
Castillo-Chavez C., Cooke K., Huang W., and Levin S.A. (1989). On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). Part 1. Single population models, J Math Biology, in press.
Curran J.W., Laurence D.N., Jaffe H.W. et. al. (1984). Acquired immunodeficiency syndrome ( AIDS) associated with transfusion, N Engl J Med 310, 69–75.
Curran J.W., Morgan W.M., Hardy A.M., Jaffe H.W., Darrow W.W. and Dowdle W.R. (1985). The epidemiology of AIDS: Current status and future prospects, Science 229, 1352–1357.
Centers for Disease Control (1984). Declining rates of rectal and pharangeal gonorrhea among males–New York City, MMWR 33, 295–297.
Centers for Disease Control (1985a). Update: AIDS in San Francisco Cohort Study, 1978–1985, MMWR 34, 573–575.
Centers for Disease Control (1985b). Self-reported behavioral change among gay and bisexual men–San Francisco, MMWR 34, 613–615.
Centers for Disease Control (1986a). HTLV III/LAV antibody prevalence in U.S. military recruit applicants, MMWR 35, 421–424.
Centers for Disease Control (1986b). AIDS among blacks and Hispanics–United States, MMWR 35, 655–666.
Centers for Disease Control (1986c). Update: Acquired Immunodeficiency Syndrome–United States, MMWR 35, 757–766.
Centers for Disease Control (1986d). Transfusion-associated HTLV-III/LAV from a seronegative donor–Colorado, MMWR 35, 389–391.
De Gruttola V. and Mayer K.H. (1987). Assessing and modeling heterosexual spread of the HIV in the United States, Reviews of Infectious Diseases 10, #1, 138–150.
Dietz K. (1987). On the transmission dynamics of HIV, preprint, 39 pages. Gallo R.C. (1987). The AIDS virus, Scientific American, January 1987, 47–56.
Gallo R. C. (1987). The AIDS virus, Scientific Ameriacn, January 1987, 47–56
Goedert J.J., Biggar R.J., Weiss S.H. (1986). Three-year incidence of AIDS in five cohorts of HTLV-III-infected risk group members, Science 231, 992–995.
Hahn B.H., Shaw G.M., Taylor M.E., Redfield R.R., Markham P.D., Salahuddin S.Z., Wong-Staal F., Gallo R.C., Parks E.S., Parks W.P. (1986). Genetic variation in HTLV-III/LAV over time in patients with AIDS or at risk for AIDS, Science 232, 1548–1553.
Hethcote H.W. (1978). An immunization model for a heterogeneous population, Theor Pop Biol 14, 338–349.
Hethcote H.W. (1983). Measles and rubella in the United States, Am J. Epid 117, 2–13.
Hethcote H.W., Stech H.W. and van den Driessche P. (1981). Periodicity and stability in epidemic models: a survey, in Differential Equations and Applications in Ecology, Epidemics and Population Problems, S. Busenberg and K.L. Cooke, Eds. Academic Press, New York, 65–82.
Hethcote H.W. and Theime H. (1985). Stability of the endemic equilibrium in epidemic models with subpopulations, Math Biosci 75, 205–227.
Hethcote H.W. and Van Ark J.W. (1987). Epidemiological models for heterogeneous populations: Proportionate mixing, parameter estimation and immunization programs, Math Biosci 84, 85–118.
Hethcote H.W., Yorke J.A. and Nold A. (1982). Gonorrhea modeling: a comparison of control methods, Math Biosci 58, 93–109.
Hethcote H.W. and Yorke J.A. (1984). Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomathematics 56, Springer-Verlag, Berlin.
Hyman J.M. and Stanley E.A. (1988). Using mathematical models to understand the AIDS epidemic, Math Biosciences, to appear.
Jacquez J.A., Koopman J., Sattenspiel L., Simon C., and Perry T. (1988). Modeling and analysis of HIV transmission: The role of contact patterns, preprint, 48 pages.
Knox E.G. (1986). A transmission model for AIDS, Eur J Epidem 2, #3, 165–177.
Lajmanovich A. and Yorke J.A. (1976). A deterministic model for gonorrhea in a nonhomogeneous population, Math Biosci 28, 221–236.
Laurence J. (1986). AIDS: Definition, epidemiology and etiology, Laboratory Medicine 17, 659–663.
Liu K.-J., Lawrence D.N., Morgan W.M., Peterman T A, Haverkos H.W., and Bregman D.J. (1986). A model-based approach for estimating the mean incubation period of transfusion-associated acquired immunodeficiency syndrome, Proc Nat Acad Sci 83, 3051–3055.
May R.M. and Anderson R.M. (1987). Transmission dynamics of HIV infection, Nature 326, 137–142.
McKusick L., Horstman W., and Coates T.J. (1985). AIDS and sexual behavior reported by gay men in San Francisco, Am J Public Health 75, 493–496.
Peterman T.A., Drotman D.P. and Curran J.W. (1985). Epidemiology of the acquired immunodeficiency syndrome ( AIDS ), Epidemiologic Reviews 7, 1–21.
Peterman T.A., Jaffe H.W., Feorino P.M., Getchall J.P., Warfield D.T., Haverkos H.W., Stoneburner R.L., and Curran J.W. (1985). Transfusion-associated acquired immunodeficiency syndrome in the United States, JAMA 254, 2913–2917.
Pickering J., Wiley J.A., Padian N.S., Lieb L.E., Echenberg D.F., and Walker J. (1986). Modeling the incidence of AIDS in San Francisco, Los Angeles and New York, Math Modeling 7, 661–688.
Redfield R.R., Wright D.C. and Tramont E.C. (1986). The Walter Reed staging classification for HTLV-III/LAV infection, N Engl J Med 314, 131–132.
Sivak S.L. and Wormser G.P. (1985). How common is HTLV—III infection in the United States? Correspondence N Engl J Med 313, 1352.
Yorke J.A., Hethcote H.W., and Nold A. (1978). Dynamics and control of the transmission of gonorrhea, Sexually Transmitted Diseases 5, 51–56.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hethcote, H.W. (1989). A Model for HIV Transmission and AIDS. In: Castillo-Chavez, C., Levin, S.A., Shoemaker, C.A. (eds) Mathematical Approaches to Problems in Resource Management and Epidemiology. Lecture Notes in Biomathematics, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46693-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-46693-9_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51820-4
Online ISBN: 978-3-642-46693-9
eBook Packages: Springer Book Archive