×
Tan, W. Y.; Zhu, X.

A stochastic model of the HIV epidemic for heterosexual transmission involving married couples and prostitutes. I: The probabilities of HIV transmission and pair formation. (English) Zbl 0885.92032

Math. Comput. Modelling 24, No. 11, 47-107 (1996).
Summary: To assess effects of risk factors on the HIV epidemic by heterosexual transmission and the role of prostitutes, we consider four populations and derive the probabilities of HIV infection in these populations. The four populations considered are the single males, the single females, the married couples, and the prostitutes. It is shown that prostitutes form a stepping stone for the HIV epidemic by heterosexual transmission. Thus, in a society in which homosexual transmission and IV drug use are not frequent, the HIV epidemic can hardly be maintained without prostitutes.

Cited in 1 Review
Cited in 8 Documents

MSC:

92D30 Epidemiology
65C20 Probabilistic models, generic numerical methods in probability and statistics
60K99 Special processes

Keywords:

mixing pattern; pair formation; sexual activity level; heterosexual transmission; prostitutes
Cite Review PDF
Full Text: DOI

References:

[1] (Global Programme On AIDS. Global Programme On AIDS, Current and future dimensions of the HIV/AIDS pandemic: A capsule summary (April, 1991), World Health Organization: World Health Organization Geneva 27, Switzerland)
[2] Brown, T.; Xenos, P., AIDS in Asia: The gathering storm, (Asia Pacific Issues (August 1994), Analysis from the East-West Center No. 16, East-West Center, University of Hawaii: Analysis from the East-West Center No. 16, East-West Center, University of Hawaii Honolulu, HI)
[3] Tan, W. Y.; Byers, R. H., A stochastic model of the HIV epidemic and the HIV infection distribution in a homosexual population, Math. Biosciences, 113, 115-143 (1993) · Zbl 0767.92027
[4] CDC, 1993 revised classification system for HIV infection and expanded surveillance case definition for AIDS among adolescents and adults, MMWR, 41 (1992), (RR-17)
[5] Tan, W. Y.; Tang, S. C.; Lee, S. R., Effects of randomness of risk factors on the HIV epidemic in homosexual populations, SIAM J. App. Math., 55, 1697-1723 (1995) · Zbl 0835.60084
[6] Mode, C. J.; Gollwitzer, H. E.; Salsburg, M. A.; Sleeman, C. K., A methodological study of a nonlinear stochastic model of an AIDS epidemic with recruitment, IMA J. Math. Appl. Med. & Biol., 6, 179-200 (1989) · Zbl 0685.92011
[7] Tan, W. Y., A chain multinomial model of the HIV epidemic in homosexual populations and the effects of randomness of the number of sexual partners, (Arino, O.; Axelrod, D. E.; Kimmel, M., Mathematical Population Dynamics 3 (1995), Wuerz Publishing Ltd: Wuerz Publishing Ltd Winnipeg, Manitoba, Canada) · Zbl 0795.92026
[8] Jacquez, J. A.; Simon, C. P.; Koopman, J.; Sattenspiel, L.; Perry, T., Modelling and analyzing HIV transmission: The effect of contact patterns, Math. Biosciences, 92, 119-199 (1988) · Zbl 0686.92016
[9] S. Busenberg, K. Cooke and Y.-H. Hsieh, A model for HIV in Asia, Math. Biosciences; S. Busenberg, K. Cooke and Y.-H. Hsieh, A model for HIV in Asia, Math. Biosciences · Zbl 0833.92016
[10] Becker, N. G.; Egerton, L. R., A transmission model for HIV with application to the Australian epidemic, Math. Biosciences, 119, 205-224 (1994) · Zbl 0792.92021
[11] Hyman, J. M.; Stanley, E. A., The effect of social mixing patterns on the spread of AIDS, (Levin, S., Mathematical Approaches to Problems in Resource Management and Epidemiology. Proceedings. Mathematical Approaches to Problems in Resource Management and Epidemiology. Proceedings, Ithaca. Mathematical Approaches to Problems in Resource Management and Epidemiology. Proceedings. Mathematical Approaches to Problems in Resource Management and Epidemiology. Proceedings, Ithaca, Lecture Notes in Biomathematics, Volume 81 (1987)), 190-219 · Zbl 0684.92017
[12] Tan, W. Y.; Tang, S. C., A stochastic model of the HIV epidemic involving both sexual contact and IV drug use, Mathl. Comput. Modelling, 17, 9, 31-57 (1993) · Zbl 0796.92025
[13] Dietz, K., On the transmission dynamics of HIV, Math. Biosciences, 90, 397-414 (1988) · Zbl 0651.92019
[14] Hadeler, K. P., Structural population models for HIV infection pair formation and non-constant infectivity, (Jewell, N. P.; Dietz, K.; Farewell, V. T., AIDS Epidemiology: Methodological Issues (1992), Birkhäuser: Birkhäuser Basel), 156-174
[15] Waldstätter, R., Pair formation in sexually-transmitted diseases,, (Castillo-Chavez, Mathematical and Statistical Approaches to AIDS Epidemiology. Mathematical and Statistical Approaches to AIDS Epidemiology, Lect. Notes in Biomath., Volume 83 (1989), Springer-Verlag: Springer-Verlag Berlin), 260-274 · Zbl 0682.00023
[16] Doll, L., Persistence of high risk sexual behavior in homosexual/bisexual men: A multicenter study, (Presented at the Fifth International AIDS Conference. Presented at the Fifth International AIDS Conference, Montreal, Quebec, Canada (June 4-9, 1989))
[17] Satten, G.; Longini, I. M., Estimation of incidence of HIV infection using cross-sectional marker survey, Biometrics, 50, 675-688 (1994) · Zbl 0822.62094
[18] Turner, B. J.; Kelly, J. V.; Ball, J. K., A severity classification system for AIDS hospitalizations, Medical Care, 27, 423-437 (1989)
[19] U. S. Bureau of the Census, Statistical Abstract of the United States (1991), U.S. Government Publication
[20] Bailey, T. J., Estimating HIV incidence and AIDS projections: Prediction and validation in the public health modelling of HIV/AIDS, Stat. in Med., 13, 1933-1943 (1994)
[21] Anderson, R. M.; Blythe, S. P.; Gupta, S.; Konings, E., The transmission dynamics of the human immunodeficiency virus type I in the male homosexual community in the United Kingdom: The influence of changes in sexual behavior, Phil. Trans. Roy. Soc. Lond. B, 325, 7-60 (1989)
[22] Tan, W. Y.; Lee, S. R.; Tang, S. C., Characterization of the HIV infection and seroconversion by a stochastic model of the HIV epidemic, Math. Biosciences, 126, 81-123 (1995) · Zbl 0822.92020
[23] Longini, I. M.; Byers, R. H.; Hessol, N. A.; Tan, W. Y., Estimation of the stage-specific numbers of HIV infections via a Markov model and backcalculation, Statistics in Medicine, 11, 831-843 (1992)
[24] CDC, (HIV/AIDS surveillance report (December 1994), The Centers of Disease Control and Prevention: The Centers of Disease Control and Prevention Atlanta, GA)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.