Traveling wave solutions of a nonlocal dispersal SIRS model with spatio-temporal delay

摘要

This paper is mainly concerned with the existence and nonexistence of traveling wave solutions of a nonlocal dispersal SIRS model with nonlocal delayed transmissions. We find that the existence and nonexistence of traveling wave solutions are determined by the critical wave speed c*. More specifically, we establish the existence of traveling wave solutions for every wave speed c > c* and R-0 > 1 by means of upper-lower solutions and Schauder's fixed point theorem. Nonexistence of traveling wave solutions is obtained by Laplace transform for any wave speed c epsilon (0, c*) and R-0 > 1.