Existence and non-existence of traveling wave solutions for a nonlocal dispersal SIR epidemic model with nonlinear incidence rate. (June 2018) - Zhou, Jiangbo; Xu, Jing; Wei, Jingdong; Xu, Haimei
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 R 0 and the minimal wave speed c ∗ . For R 0 > 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 R 0 > 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 R 0 = 1 with c > 0 and R 0 < 1 with c > 0, the non-existence theorems are also established.