Equilibrium Analysis of a Mathematical Model for the Spread of AIDS in a Two Sex Population with Mixing Constraints

Abstract

For a mathematical model for the spread of HIV by sexual transmission in a heterosexual population we analyse the existence and stability of equilibrium solutions. The model is designed to investigate the effects of a fundamental constraint in any social/sexual mixing process for heterogeneous populations. The group contact constraint conserves the number of new sexual partnerships formed per unit time between the sexes, and will have at least a quantitative influence on the dynamics of the model. The analysis has been carried out for general and specific forms of the sexual activity rates (the mean number of sexual partners per unit time for a typical individual). In general we define a threshold parameter R0, the Reproductive Number, which is a key determinant of the behaviour of the model. We show that in general if R0>1 there is at least one endemic equilibrium. The specific cases of a dominance sexual activity rate and proportional sexual activity rates are discussed in more detail. Multiple endemic equilibria can occur for the former but not the latter.