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.


92D25 Population dynamics (general)
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.