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A discrete branching process model for the spread of HIV via steady sexual partnerships

Journal of Mathematical Biology volume 48, pages 423–443 (2004)Cite this article

Abstract.

The transmission of HIV in a monogamous heterosexual population structured by the ordinal number of the current partnership is considered. The sexual carreer of a man (woman) is thought to be a succession of k(m) partnerships, and a multitype Galton-Watson process is defined, in which the objects are infections and the types are related to the ordinal number of the partnership during which a person has acquired the infection. Contrary to multitype models in which the types are not age-related in some sense, this process contains at least two singular types, namely infections acquired in the last partnership of a man or a woman. The criticality parameter of this branching process is the epidemic threshold parameter R 0 . In the case k=m an epidemic is impossible, however large k may be, if the difference between the ordinal numbers of the partners in a pair is never > 1. When the frequency of pairs in which this difference is ≥ 2 increases, then R 0 increases. This is demonstrated for the cases k=m=3 and k=4,m=3. The formulae obtained show also the joint influence of the mixing pattern and of variable infectivity. The result for the case of uniform mixing implies that a formula of May and Anderson (1987) is an approximation for k and m large.

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  1. Department of Basic Sciences, Escuela Colombiana de Ingenieria, Autopista Norte, km 13, Bogotà, Colombia

    Helmut Knolle

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  1. Helmut Knolle
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Mathematics Subject Classification (2000): 92D (primary), 60J (secondary)

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Knolle, H. A discrete branching process model for the spread of HIV via steady sexual partnerships. J. Math. Biol. 48, 423–443 (2004). https://doi.org/10.1007/s00285-003-0241-7

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  • DOI: https://doi.org/10.1007/s00285-003-0241-7

Key words or phrases

  • Epidemic threshold theorem
  • R 0
  • AIDS
  • Partnership
  • Age
  • Galton-Watson process