Periodic Traveling Wave Solutions of Time-Periodic SIR Epidemic Models With External Supplies

Abstract

The existence and non-existence of periodic traveling wave solutions of a class of time-periodic SIR epidemic models with external supplies are considered. Firstly, by constructing appropriate upper and lower solutions of the auxiliary system and defining a closed convex cone, the existence of periodic traveling waves is transformed into a fixed point problem of the non-monotone operator defined on the closed convex cone. The existence of periodic solutions for the auxiliary system is established by Schauder fixed point theorem, and Arzela-Ascoli theorem is used to prove the existence of periodic traveling waves for the original model. Secondly, the non-existence of periodic traveling waves is obtained by analysis techniques.