Abstract
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 0<c<c∗, the non-existence theorem is derived by applying the two-sided Laplace transform and making full use of the structure of the model. For R0=1 with c>0 and R0<1 with c>0, the non-existence theorems are also established.
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