Spatiotemporal propagation of a time‐periodic reaction–diffusion SI epidemic model with treatment

Abstract

AbstractThis work is concerned with the spatiotemporal propagation phenomena for a time‐periodic reaction‐diffusion susceptible‐infectious (SI) epidemic model with treatment in terms of the asymptotic speed of spread and periodic traveling waves. First, the asymptotic speed of spread is characterized and the spreading properties of the model are analyzed by combining the periodic principal eigenvalue problem, comparison method, and the uniform persistence idea for a dynamical system. Second, by constructing suitable super‐ and subsolutions for truncation problems corresponding to the traveling wave system, the existence of periodic traveling waves is established via the fixed point theorem twice. It turned out that the asymptotic speed of spread coincides with the minimum wave speed of periodic traveling waves. Finally, via numerical simulation, the effects of some important parameters (such as diffusion rate, treatment rate, etc.) on the spreading speed are discussed, and the asymptotic properties of the periodic traveling waves are explored.