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Traveling wave solutions for a delayed diffusive SIR epidemic model with nonlinear incidence rate and external supplies. (English) Zbl 1362.92088
Summary: In this paper, we study the traveling wave solutions of a delayed diffusive SIR epidemic model with nonlinear incidence rate and constant external supplies. We find that the existence of traveling wave solutions is determined by the basic reproduction number of the corresponding spatial-homogenous delay differential system and the minimal wave speed. The existence is proved by applying Schauder’s fixed point theorem and Lyapunov functional method. The non-existence of traveling waves is obtained by two-sided Laplace transform.

MSC:
92D30 Epidemiology
35K57 Reaction-diffusion equations
35C07 Traveling wave solutions
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