On the uniqueness of the positive solution of an integral equation which appears in epidemiological models

In this paper, we show that the positive solution of a nonlinear integral e quation which appears in classical SIR epidemiological models is unique. Th e demonstration of this fact is necessary to justify the correctness of any approximate or numerical solution. The SIR epidemiological model is used only for simplicity. In fact, the met hods used can be easily extended to prove the existence and uniqueness of t he more involved integral equations that appear when more biological realit ies are considered. Thus the inclusion of a latent class (SLIR models) and models incorporating variability in the infectiousness with duration of the infection and spatial distribution lead to integral equations to which the results derived in this paper apply immediately.