Analytical and Numerical Results for the Age-Structured S-I-S Epidemic Model with Mixed Inter-Intracohort Transmission

Abstract

A model which describes the dynamics of an $S \to I \to S$ epidemic in an age-structured population at the steady state is considered. The model consists of a nonlinear and nonlocal system of equations of hyperbolic type and has already been partly analyzed by other authors. Here, a special form for the force of infection is considered. Explicitly computable threshold conditions are given, and some regularity results for the solutions are proven. An implicit finite difference method of characteristics to approximate the solutions is used. Optimal error estimates are derived and results from numerical simulations are presented. The discrete dynamical system arising from the numerical algorithm, is also analyzed, showing that it shares many properties of the continuous model.