Wave propagation in a diffusive SIR epidemic model with spatiotemporal delay

Abstract

In this paper, we propose a SIR epidemic model incorporating Laplacian diffusion and the spatiotemporal delay to model the transmission of communicable diseases. The existence and nonexistence of traveling wave solutions for the model are investigated. It is found that the threshold dynamics are determined by the basic reproduction number and the minimum wave speed c∗. By introducing an auxiliary system and Schauder's fixed point theorem, we establish the existence of traveling wave solutions for the model if and c > c∗. Employing Fubini theorem and the two‐sided Laplace transform, we obtain the nonexistence of traveling wave solutions for the model if or 0 < c < c∗. Our results cover and improve some results in the literature.