Advertisement

Modeling Heterogeneity in Susceptibility and Infectivity for HIV Infection

  • N. Scott Cardell
  • David E. Kanouse
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 83)

Abstract

Models of the spread of human immunodeficiency virus (HIV) infection must deal with substantial heterogeneity in the populations at risk. The virus is spread by behaviors that are far from uniformly distributed in the population, and substantial variations in biological aspects of susceptibility and infectivity are also likely. How adequately a model represents this heterogeneity will substantially determine its accuracy and usefulness for capturing the dynamics of the epidemic, for making forecasts of future spread, and for answering questions of policy interest.

There are two main ways in which a model may handle heterogeneity: by partitioning the population into discrete risk groups that are in some respect homogeneous within group but heterogeneous between groups, and by introducing model parameters to capture the effects of heterogeneity in a group or in the population as a whole. This paper discusses the dynamics of heterogeneity in HIV spread and develops a theory of heterogeneity in susceptibility and infectivity within a population that allows a simple representation of key phenomena within an epidemic model. It is suggested that the effects of heterogeneity-related phenomena can be captured by letting two key parameters, the mean susceptibility over time of the uninfected and the mean infectivity of the infected, depend upon X/P, the proportion of the population that is uninfected. (The mean infectivity may also depend on the cumulative proportion of the population that is removed through death or other causes). Because X/P, aswe define it, is monotonic over time, this approach is general, and it allows considerable flexibility in the choice of functional form to fit available data.

Keywords

Human Immunodeficiency Virus Human Immunodeficiency Virus Infection Risky Behavior Epidemic Model Susceptibility Variation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blythe, S.P. and R.M. Anderson. (1988). Distributed incubation and infectious periods in models of the transmission dynamics of the human immunodeficiency virus (HIV). IMA J. Math. Biol. Med., 5, 1–19.MathSciNetMATHCrossRefGoogle Scholar
  2. Blythe, S.P. and C. Castillo-Chavez. (1989). Like-with-like preference and sexual mixing models. Submitted, Math. Biosci. Google Scholar
  3. Cardeil, N.S., D.E. Kanouse, E.M. Gorman, C. Serrato, P.H. Reuter, and A.P. Williams. (1987). Modeling the spread of human immunodeficiency virus in the United States. Presented to III International Conference on AIDS, Washington, D.C.Google Scholar
  4. Castillo-Chavez, C., K. Cooke, W. Huang, and S.A. Levin. (1989). The role of long periods of infectiousness in the dynamics of acquired immunodeficiency syndrome (AIDS). In Mathematical Approaches to Resource Management and Epidemiology. In press, Lecture Notes in Biomathematics, Springer-Verlag.Google Scholar
  5. Curran, J.W., H.W. Jaffe, A.M. Hardy, M. Morgan, R.M. Selik, and T.J. Dondero. (1988). Epidemiology of HIV infection and AIDS in the United States. Science, 239, 610–616.CrossRefGoogle Scholar
  6. Friedland, G.H, and R. S. Klein. (1987). Transmission of the human immunodeficiency virus. N. Engl. J. Med., 317, 1125–1135.CrossRefGoogle Scholar
  7. Hethcote, H.W. (1976). Qualitative analysis of communicable disease models. Math Biosciences, 28, 335–356.MathSciNetMATHCrossRefGoogle Scholar
  8. Hethcote, H.W. and J.W. Van Ark. (1987). Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs. Math. Biosci., 84, 85–118.MathSciNetMATHCrossRefGoogle Scholar
  9. Hethcote, H.W. and J.A. Yorke. (1984). Gonorrhea, transmission dynamics and control. Lecture Notes in Biomathematics 56, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo.Google Scholar
  10. Hyman, J.M. and E.A. Stanley. (1988). Using mathematical models to understand the AIDS epidemic. Math. Biosci., 90, 415–473.MathSciNetMATHCrossRefGoogle Scholar
  11. Jacquez, J.A., C.P. Simon, J. Koopman, L. Sattenspiel, and T. Perry. (1988). Modeling and analyzing HIV transmission: the effect of contact patterns. Math. Biosci., 92, 119–199.MathSciNetMATHCrossRefGoogle Scholar
  12. Nold, A. (1980). Heterogeneity in diseases-transmission modeling. Math. Biosci., 52, 227–240.MathSciNetMATHCrossRefGoogle Scholar
  13. Padian, N., J. Wiley, and W. Winkelstein. (1987). Male to female transmission of human immunodeficiency virus (HIV): Current results, infectivity estimates, and San Francisco population seroprevalence estimates. Presented to III International Conference on AIDS, Washington, D.C.Google Scholar
  14. Sattenspiel, L. and C.P. Simon. (1988). The spread and persistence of infectious diseases in structured populations. Math. Biosci., 90, 341–366.MathSciNetMATHCrossRefGoogle Scholar
  15. Turner, C.F., H.G. Miller, and L.E. Moses (eds.). (1989). AIDS: Sexual Behavior and Intravenous Drug Use. National Academy Press, Washington, D.C.Google Scholar
  16. Wiley, J. (1987). Models for estimation of transmission probabilities of HIV in epidemiologic studies. Presented at Conference on Statistical and Mathematical Modeling of the AIDS Epidemic, Johns Hopkins University, Baltimore, MD.Google Scholar
  17. Wiley, J.A., S.J. Herschkorn, and N.S. Padian. (1989). Heterogeneity in the probability of HIV transmission per sexual contact: The case of male-to-female transmission in penile-vaginal intercourse, Stat. Med., 8, 93–102.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • N. Scott Cardell
    • 1
  • David E. Kanouse
    • 2
  1. 1.Washington State UniversityPullmanUSA
  2. 2.The RAND CorporationSanta MonicaUSA

Personalised recommendations