A family of mathematical models to describe the risk of infection by a sexually transmitted agent.

Several recent publications have used, without demonstrating its derivation, a mathematical model that describes the risk of being infected by a sexually transmitted agent as a function of four parameters: the number of partners, the number of contacts with each partner, the per-contact probability of transmission, and the probability of a partner being infected. The model is derived both from elementary probability concepts and, more formally, by using the binomial expansion and conditional probabilities. The assumptions involved in these derivations are brought out, as are the limitations they impose on the uses of the model. The model equations used so far in published studies are shown to be special cases of a general form that allows for more variability of the sexual behavior modeled. The different uses to which the model has been put are categorized, and some further ones are suggested.