Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate

Abstract EN

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 analyzsis, 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.