Existence and non-existence of traveling wave solutions for a nonlocal dispersal SIR epidemic model with nonlinear incidence rate

A nonlocal dispersal SIR epidemic model with nonlinear incidence rate is introduced. It is shown that the existence and non-existence of nontrivial and nonnegative traveling wave solutions of this model are fully determined by the threshold values, that is, the basic reproduction number R0 and the minimal wave speed c∗. For R0>1 and c≥c∗, the existence theorem is obtained by the method of auxiliary system, Schauder's fixed point theorem and three limiting arguments. For R0>1 and 00 and R0<1 with c>0, the non-existence theorems are also established.