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 Ro 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 R-0 > 1 and c > c*, and the nonexistence of traveling waves for R-0 > 1 and 0 < c < c*. Some numerical simulations and discussions are also provided to illustrate our analytical results. (C) 2017 Elsevier Ltd. All rights reserved.