A simple model of human and animal trypanosomiasis is proposed in which the Ross equation for disease transmission is supplemented by a differential equation describing the inheritance of susceptibility in the vector. The model predicts an equilibrium state of balanced polymorphism for the fraction, θ, of susceptible tsetse and the occurrence of periodic epidemics at roughly the observed intervals. A loss of infectivity to tsetse of mechanically transmitted strains of trypano some would seem to be a good evolutionary strategy for the trypanosome. The main implication for disease control is that measures initially reducing trypanosomiasis incidence could trigger off subsequent epidemics. Since θ leads incidence, monitoring θ could give several years advance warning of major epidemics.
