Special Session 24: Qualitative analysis of reaction diffusion systems
Contents
This talk is concerned with traveling wave solutions of a nonlocal dispersal SIR epidemic model. We show that our results on existence and nonexistence of traveling wave solutions are determined by the basic reproduction number of the corresponding ordinary differential model and the minimal wave speed. This threshold dynamics is proved by constructing an invariant cone and applying Schauder's fixed point theorem on this cone and the Laplace transform. The main difficulties are that a lack of regularizing effect occurs and the order-preserving property of this model loses.