Mathematical models of HIV infection. I. Threshold conditions for transmission and host survival.

This is the second in a series of papers modeling human immunodeficiency virus (HIV) infections at four levels: transmission, interaction with the immune system, gene regulation, and selection of mutants. In the previous paper (1) we described and presented a theory of the HIV cytopathic effect based upon the models (and a review of the literature). In this article we give mathematical equations of threshold conditions that connect infectivity, length of host survival, and frequency of acts conducive to transmission. The formula is derived not only for homogeneous populations but also for populations of an arbitrary number of subgroups with varying frequencies of risk behavior, varying rates of infection and latency periods, and varying frequencies of interaction with other groups.