Homogeneous models for sexually transmitted diseases

Abstract

A system of eight ordinary differential equations describes birth, death, formation of pairs, separation, and transmission of a sexually transmitted disease. Here, in contrast to an earlier version of the model by Dietz and Hadeler, the recruitment process is coupled to the actual population size. Nevertheless, as in most demographic models, the equations are assumed homogeneous. There is a noninfected exponentially growing persistent solution which is stable (in the sense of the stability theory for homogeneous equations) for low rates of pair formation and low infectivity. If these parameters are increased, this state may lose stability, a stable persistent solution describing an infected population bifurcates. The exact bifurcation thresholds are derived in terms of the epidemiologically relevant parameters. © 1990 Rocky Mountain Journal of Mathematics.