Qualitative Behavior of Numerical Solutions to an S-I-S Epidemic Model

Abstract

A finite difference scheme along the characteristics is used to approximate the solution of an age-dependent s-i-s epidemic model. The global behavior of the discrete solution resulting from the algorithm is investigated. It is shown that a nontrivial discrete periodic solution is generated by a periodic force of infection. Sufficient (and explicit) threshold conditions for the existence and stability of a unique nontrivial periodic solution are given. Results from numerical experiments are presented. © 1998 John Wiley & Sons, Inc.