A generalized chain binomial model with application to HIV infection

The original Reed-Frost formulation of the chain binomial model is mathematically equivalent to a stochastic model allowing a Poisson number of effective contacts in a time interval. Their formulation cannot accommodate survey data that necessarily correspond to more complex distributions of partners or contacts, or to large populations where complete random mixing is unlikely. This paper generalizes the Reed-Frost model to accommodate these situations in both the one- and two-population settings. The extension to multiple populations is also outlined. Using the model to predict HIV incidence in San Francisco's homosexual population, we show that the total number of contacts over all partners is more important than the distribution of contacts among partners in determining the number of infected.