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Existence of traveling waves for a delayed SIRS epidemic diffusion model with saturation incidence rate. (English) Zbl 1406.92647

Summary: This paper is concerned with the existence of traveling waves for a delayed SIRS epidemic diffusion model with saturation incidence rate. By using the cross-iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions. By careful analysis, we derive the existence of traveling waves connecting the disease-free steady state and the endemic steady state through the establishment of the suitable upper-lower solutions.

MSC:

92D30 Epidemiology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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