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On the transmission dynamics of HIV. (English) Zbl 0651.92019
Summary: The classical models for sexually transmitted diseases implicitly assume that all contacts with the same partner are concentrated in one instant. A new model is presented which takes into account the duration of a partnership and the number of contacts with the same partner. An explicit formula is given for the number of partners during a lifetime which is necessary to maintain the infection at an endemic level. The present basic model may serve as a building block in more realistic models for the spread of HIV in the population.

MSC:
92D25 Population dynamics (general)
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[1] Dietz, K.; Schenzle, D., Mathematical models for infectious disease statistics, (), 167-204 · Zbl 0586.92017
[2] Hethcote, H.W.; Yorke, J.A., Gonorrhea transmission dynamics and control, () · Zbl 0542.92026
[3] Ravenholt, R.T., Role of hepatitis B virus in acquired immunodeficiency syndrome, Lancet, 2, 885-886, (1983)
[4] Dietz, K., Models for parasitic disease control, Bull. internat. statist. inst., 46, 531-544, (1975)
[5] Anderson, R.M.; Medley, G.F.; May, R.M.; Johnson, A.M., A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS, IMA J. math. appl. med. biol., 3, 229-263, (1986) · Zbl 0609.92025
[6] Kieβling, D.; Stannat, S.; Schedel, I.; Deicher, H., Überlegungen und hochrechnungen zur epidemiologie des “acquired immunodeficiency syndrome” in der bundesrepublik deutschland, Infection, 14, 217-222, (1986)
[7] Knox, E.G., A transmission model for AIDS, European J. epidemiol., 2, 165-177, (1986)
[8] Kolb, I., Das kreuz mit der liebe, (1980), Gruner & Jahr Hamburg
[9] Dietz, K.; Hadeler, K.P., Epidemiological models for sexually transmitted diseases, J. math. biol., 26, 1-25, (1988) · Zbl 0643.92015
[10] Peterman, T.A.; Stoneburner, R.L.; Allen, J.R.; Joffe, H.W.; Curran, J.W., Risk of HIV transmission from heterosexual adults with transfusion associated infections, J. amer. med. assoc., 259, 55-58, (1988)
[11] Dietz, K., The dynamics of spread of HIV infection in the heterosexual population, (), 77-105
[12] Dannecker, M.; Reiche, R., Der gewöhnliche homosexuelle. eine soziologische untersuchung über männliche homosexuelle in der bundesrepublik, (1974), S. Fischer Frankfurt a.M
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