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Journal of Theoretical Medicine
Volume 2 (2000), Issue 4, Pages 285-296
http://dx.doi.org/10.1080/10273660008833055

A Mathematical Model of HIV Transmission in Homosexuals with Genetic Heterogeneity

Institut für Mathematische Statistik und Versicherungslehre (IMSV), Universität Bern, 3012 Bern, Switzerland

Received 22 November 1998; Accepted 9 August 1999

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 △32 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. Based on available data, we propose a one-sex model with susceptibles classified as having no, partial or full natural resistance to HIV infection, and infecteds classified as rapid, normal or slow progressors. Our goals are to investigate the impact of such heterogeneity on the spread of HIV and to identify key parameters. The basic reproductive number R0 is derived from a simplified model. The relative contributions to R0 from the three groups of infecteds are investigated. We present a rough estimating procedure making use of limited data to estimate some new parameters specific to our model. Finally the rough estimating procedure is applied to an example focusing on CCR5-△32 in San Francisco gay men. The relative contributions to R0 among the three infected groups are compared using two different classifying criteria for infecteds. Under given assumptions, we conclude that, without any intervention, HIV infection will continue to spread in this population and the epidemic is mainly driven by the normal progressors. The transmission rates from infecteds are identified as key parameters.