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Effects of Genetic Heterogeneity on HIV Transmission in Homosexual Populations

  • Shu-Fang Hsu Schmitz
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 126)

Abstract

Several AIDS cohort studies observe that the incubation period between HIV infection and AIDS onset can be shorter than 3 years in about 10% seropositive individuals, or longer than 10 years in about 10–15% individuals. On the other hand, many individuals remain seronegative even after multiple exposures to HIV. These distinct outcomes have recently been correlated with some mutant genes in HIV co-receptors (e.g., CCR5, CCR2 and CXCR4). For instance, the mutant alleles Δ32 and m303 of CCR5 may provide full protection against HIV infection in homozygotes and partial protection in heterozygotes; moreover, infected heterozygotes may progress more slowly than individuals who have no mutant alleles. Frequencies of these mutant alleles are not very low in Caucasian populations, therefore their effects may not be insignificant. To investigate the impact of such heterogeneity on the spread of HIV, Hsu Schmitz (2000a,2000b), based on available data, proposes a specific type of models where susceptibles are classified as having no, partial or full natural resistance to HIV infection and infecteds as rapid, normal or slow progressors. She also applies the models to CCR5-Δ 32 mutation in San Francisco gay men. This manuscript sketches her models with focus on the basic model without treatment and an extended model with treatment in certain proportion of newly infected individuals. The same example of CCR5-Δ 32 in San Francisco gay men is used, but some parameters are estimated in different ways. The results are very similar to those in Hsu Schmitz (2000a,2000b) with the following two main conclusions: 1) without any intervention, HIV infection will continue to spread in this population and the epidemic is mainly driven by the normal progressors; 2) treating only a certain proportion of newly infected individuals with currently available therapies is unlikely to eradicate the disease. Additional interventions are thus necessary for disease control.

Key words

HIV AIDS mathematical model R0 homosexual mutation CCR5 treatment 

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References

  1. [1]
    Anderson R.M., Gupta, S., and May, R.M. Potential of community-wide chemotherapy or immunotherapy to control the spread of HIV-1. Nature 350:356–359 (1991).CrossRefGoogle Scholar
  2. [2]
    Busenberg, S. and Castillo-Chavez, C. A general solution of the problem of mixing of subpopulations and its application to risk- and age-structured epidemic models for the spread of AIDS. IMA Journal of Mathematics Applied in Medicine & Biology 8:1–29 (1991).MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Coutinho, F.A.B., Massad, E., Lopez, L.F., et al. Moelling heterogeneities in individual frailties in epidemic models. Mathematical and Computer Modelling 30:97–115 (1999).MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Dean, M., Carrington, M., Winkler, C, et al. Genetic restriction of HIV-1 infection and progression to AIDS by a deletion allele of the CKR5 structural gene. Science 273:1856–1862 (1996).CrossRefGoogle Scholar
  5. [5]
    Detels, R., Liu Z., Hennessey, K., et al. Resistance to HIV-1 infection. Multicenter AIDS Cohort Study. J Acquir Immune Defic Syndr Hum Retrovirol 7:1263–1269 (1994).Google Scholar
  6. [6]
    Diekmann, O., Heesterbeek, J.A.P., and Metz, J.A.J. On the definition and the computation of the basic reproduction ratio Ro in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology 28:365–382 (1990).MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Dushoff, J. and Levin, S. The effects of population heterogeneity on disease invasion. Mathematical Biosciences 128:25–40 (1995).zbMATHCrossRefGoogle Scholar
  8. [8]
    Faure, S., Meyer, L., Costagliola, D., et al. Rapid progression to AIDS in HIV+ individuals with a structural variant of the chemokine receptor CX3CR1. Science 287:2274–2277 (2000).CrossRefGoogle Scholar
  9. [9]
    Fowke, K.R., Nagelkerke, N.J.D., Kimani, J., et al. Resistance to HIV-1 infection among persistently seronegative prostitutes in Nairobi, Kenya. Lancet 348:1347–1351 (1996).CrossRefGoogle Scholar
  10. [10]
    Hsu Schmitz, S.-F. A mathematical model of HIV transmission in homosexuals with genetic heterogeneity. Journal of Theoretical Medicine 2:285–296 (2000a).zbMATHCrossRefGoogle Scholar
  11. [11]
    Hsu Schmitz, S.-F. Treatment and vaccination against HIV/AIDS in homosexuals with genetic heterogeneity. Mathematical Biosciences 167:1–18 (2000b).zbMATHCrossRefGoogle Scholar
  12. [12]
    Hsu Schmitz, S.-F. Impact of changes in contact rates on HIV transmission under treatment and vaccination in homosexual populations with genetic heterogeneity (submitted) (2001).Google Scholar
  13. [13]
    Ibanez, A., Puig, T., Elias, J., et al. Quantification of integrated and total HIV- 1 DNA after long-term highly active antiretroviral therapy in HIV-1-infected patients. AIDS 13(9):1045–1049 (1999).CrossRefGoogle Scholar
  14. [14]
    Lillo, F.B., Ciuffreda, D., Veglia, F., et al. Viral load and burden modification following early antiretroviral therapy of primary HIV-1 infection. AIDS 13(7):791–796 (1999).CrossRefGoogle Scholar
  15. [15]
    Martin, M.P., Dean, M., Smith, M.W., et al. Genetic acceleration of AIDS progression by a promoter variant of CCR5. Science 282:1907–1911 (1998)CrossRefGoogle Scholar
  16. [16]
    McLean, A.R., Blower, S.M. Imperfect vaccines and herd immunity to HIV. Proc. R. Soc. Lond. B 253:9–13 (1993).CrossRefGoogle Scholar
  17. [17]
    Paxton, W.A., Martin, S.R., Tse, D., et al. Relative resistance to HIV-1 infection of CD4 lymphocytes from persons who remain uninfected despite multiple high-risk sexual exposure. Nature Medicine 2:412–417 (1996).CrossRefGoogle Scholar
  18. [18]
    Phair, J.P. Keynote address: variations in the natural history of HIV infection. AIDS REs Hum REtrovir 10:883–885 (1994).CrossRefGoogle Scholar
  19. [19]
    Quillent, C., Oberlin, E., Braun, J., et al. HIV-1-resistance phenotype conferred by combination of two separate inherited mutations of CCR5 gene. The Lancet 351:14–18 (1998).CrossRefGoogle Scholar
  20. [20]
    Rosenberg, E.S., Altfeld, M., Poon, S.H., et al. Immune control of HIV-1 after early treatment of acute infection. Nature 407:523–526 (2000).CrossRefGoogle Scholar
  21. [21]
    Samson, M., Libert, F., Doranz, B.J., et al. Resistance to HIV-1 infection in Caucasian individuals bearing mutant alleles of the CCR-5 chemokine receptor gene. Nature 382:722–725 (1996).CrossRefGoogle Scholar
  22. [22]
    Sheppard, H.W., Lang, W., Ascher, M.S. The characterization of nonprogressors: long-term HIV-1 infection with stable CD4+ T-cell levels. AIDS 7:1159–1166 (1993).CrossRefGoogle Scholar
  23. [23]
    Smith, M.W., Dean, M., Carrington, M., et al. Contrasting genetic influence of CCR2 and CCR5 variants on HIV-1 infection and disease progression. Science 277:959–965 (1997).CrossRefGoogle Scholar
  24. [24]
    Winkler, C., Modi, W., Smith, M.W., et al. Genetic restriction of AIDS pathogenesis by an SDF-1 chemokine gene variant. Science 279:389–393 (1998).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Shu-Fang Hsu Schmitz
    • 1
  1. 1.Institut für Mathematische Statistik und Versicherungslehre (IMSV)Universität BernBernSwitzerland

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