Skip to main content

Review of Recent Models of HIV/AIDS Transmission

  • Chapter
Book cover Applied Mathematical Ecology

Part of the book series: Biomathematics ((BIOMATHEMATICS,volume 18))

Abstract

HIV, the human immunodeficiency acquired immunodeficiency syndrome virus, is the etiological agent for AIDS (acquired immuno deficiency syndrome). In 1982 Gallo suggested that the cause of AIDS was likely to be a new human retrovirus and, in 1983, researchers at the Pasteur Institute under the direction of Montagnier were able to isolate a new retrovirus from a New York AIDS victim (see Barre-Sinoussi et al., 1983). In 1984, Gallo and his colleagues isolated the same type of retrovirus and proved it to be the etiological agent of AIDS (for more details see Gallo, 1986, 1987; Wong-Staal and Gallo, 1985). This virus has been estimated to kill at least 30% of those infected. By April 1988, about 58,000 individuals have died of AIDS in the United States, and the Coolfont Report (1986) predicts that by 1991 the lower bound for the cumulative number of AIDS cases will be 290,000 individuals in the United States alone. One of the biggest problems associated with HIV is that most infected individuals appear to be asymptomatic and infectious for long periods of time, with an average infectious period of at least 8 years. Furthermore, there is growing evidence that the infectiousness of individuals varies with time since infection; the amount of free virus is relatively high just after infection (Francis et al., 1984; Salahuddin et al., 1984), remains low for several years, and climbs again within a year or so of the onset of AIDS (Lange et al., 1986).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, R.M. (1988) The epidemiology of HIV infection: variable incubation plus infectious period and heterogeneity in sexual activity (ms.)

    Google Scholar 

  • Anderson, R.M., May, R.M. (1987) Transmission dynamics of HIV infection. Nature 326, 137–142

    Article  Google Scholar 

  • Anderson, R.M., et al. (1988) A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS. IMA J. Math. Med. Biol, (in press)

    Google Scholar 

  • Barre-Sinoussi, F., et al. (1983) Isolation of a T-lymphotropic retrovirus from a patient at risk for acquired immune deficiency syndrome (AIDS). Science 220, 868–70

    Article  Google Scholar 

  • Blythe, S.P., Anderson, R.M. Distributed incubation and infectious periods in models of the transmission dynamics of the Human Immunodeficiency Virus (HIV). IMA J. Math. Med. Biol, (in press)

    Google Scholar 

  • Castillo-Chavez, C., Cooke, K., Huang, W., Levin, S.A. (1988a) The role of infectious periods in the dynamics of acquired immunodeficiency syndrome (AIDS). In: C. Castillo-Chavez, S.A. Levin, and C. Shoemaker (eds.) Proceedings International Symposium in Mathematical Approaches to Ecological and Environmental Problem Solving, Ithaca, 1987. Lecture Notes in Biomathematics. Springer, Berlin Heidelberg New York (to appear)

    Google Scholar 

  • Castillo-Chavez, C., Cooke, K., Huang, W., Levin, S.A. (1988b) The role of long infectious periods in the dynamics of HIV/AIDS. Part 1 (in preparation)

    Google Scholar 

  • Castillo-Chavez, C., Cooke, K., Huang, W., Levin, S.A. (1988c) The role of infectious periods in the dynamics of in the dynamics of HIV/AIDS. Part 2 (in preparation)

    Google Scholar 

  • Colgate, S.A., Hyman, J.M., Stanley, E.A. (1988) A risk base model explaining the cubic growth in AIDS cases (unpublished manuscript)

    Google Scholar 

  • Coolfont Report (1986) A PHS plan for prevention and control of AIDS and the AIDS virus. Public Health Rep. 101, 341–48

    Google Scholar 

  • Crow, J.F., Kimura, M. (1970) An introduction to population genetics theory. Burgess Publishing Company. Minneapolis, Minnesota

    Google Scholar 

  • Dietz, K., Hadeler, K.P. (1988) Epidemiological models for sexually transmitted diseases. J. Math. Biology (in press)

    Google Scholar 

  • Francis, D.P. et al. (1984) Infection of chimpanzees with lymphadenopathy-associated virus. Lancet, 1, 1276–77

    Article  Google Scholar 

  • Fredrickson, A.G. A mathematical theory of age structure in sexual populations: random mating and monogamous marriage models. 1971. Math. Biosci. 10, 117–143

    Article  Google Scholar 

  • Gallo, R.C. (1986) The first human retrovirus. Scientific American, Dec. 88–89

    Google Scholar 

  • Gallo, R.C. (1987) The AIDS virus. Scientific American, Jan.: 47–56

    Google Scholar 

  • Hyman, J.M., Stanley, E.A., (1988) A risk base model for the spread of the AIDS virus. Math. Biosci. (in press)

    Google Scholar 

  • Kendall, D.G. (1949) Stochastic processes and population growth. J. Roy. Statist. Soc. Ser. Bll, 230–264

    MathSciNet  Google Scholar 

  • Keyfitz, N. (1972) The mathematics of sex and marriage. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. IV: Biology and Health, pp. 89–108

    Google Scholar 

  • Lange, J.M.A., et al. (1986) “Persistent HIV antigenaemia and decline of HIV core antibodies associated with transition to AIDS.” Brit. Med. J. 293, 1459–62

    Article  Google Scholar 

  • May, R.M., Anderson, R.M., McLean, A.R. (1988a) Possible demographic consequences of HIV/AIDS: I, assuming HIV infection always leads to AIDS. Math. Biosci. (in press)

    Google Scholar 

  • May, R.M., Anderson, R.M., McLean, A.R. (1988b) Possible demographic consequences of HIV/AIDS: II, assuming HIV infection does not necessarily lead to AIDS. In: Castillo-Chavez, C., Levin, S.A., Shoemaker, C. (eds.) Proceedings International Symposium in Mathematical Approaches to Ecological and Environmental Problem Solving, Berlin Heidelberg New York Ithaca, 1987. Lecture Notes in Biomathematics. Springer (to appear)

    Google Scholar 

  • Pollard, J.H. (1973) Mathematical models for the growth of human populations, Chapter 7. The University Press, Cambridge

    MATH  Google Scholar 

  • Suluhuddin, S.Z. et al. (1984) HTLV-III in symptom-free seronegative persons. Lancet, Dec. 22–29: 1418–20

    Google Scholar 

  • Wong-Staal, F., Gallo, R.C. (1985) Human T-lymphotropic retroviruses. Nature 317, 395–403

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Castillo-Chavez, C. (1989). Review of Recent Models of HIV/AIDS Transmission. In: Levin, S.A., Hallam, T.G., Gross, L.J. (eds) Applied Mathematical Ecology. Biomathematics, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61317-3_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-61317-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64789-5

  • Online ISBN: 978-3-642-61317-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics