Traveling waves in a nonlocal dispersal SIRH model with relapse

This paper is concerned with traveling wave solutions of a nonlocal dispersal Susceptible-Infective-Removal-Healing (for short SIRH ) model with relapse. It is found that the existence and nonexistence of traveling waves of the system are not only determined by the critical wave speed c∗, but also by the basic reproduction number R0 of the corresponding system of ordinary differential equations. More precisely, we use Schauder's fixed-point theorem to obtain the existence of traveling waves for R0>1 and c>c∗, and the nonexistence of traveling waves for R0>1 and 0