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The paper describes some preliminary attempts to formulate simple mathematical models of the transmission dynamics of HIV infection in homosexual communities. In conjunction with a survey of the available epidemiological data on HIV infection and the incidence of AIDS, the models are used to assess how various processes influence the course of the initial epidemic following the introduction of the virus. Models of the early stages of viral spread provide crude methods for estimating the basic reproductive rate of the virus, given a knowledge of the incubation period of the disease (AIDS) and the initial doubling time of the epidemic. More complex models are formulated to assess the influence of variation in the incubation period and heterogeneity in sexual activity. The latter factor is shown to have a major effect on the predicted pattern of the epidemic; high levels of heterogeneity decrease its magnitude …