Periodic wave propagation in a diffusive SIR epidemic model with nonlinear incidence and periodic environment

The aim of this paper is to study the periodic traveling wave solutions in a nonautonomous reaction-diffusion susceptible-infected-removed epidemic model with general nonlinear incidence and time-periodic environment. The basic reproduction number [Formula: see text] and the critical wave speed c* are defined. By the fixed-point theorem and upper–lower solutions, the sufficient conditions for the existence of traveling waves satisfying some asymptotic boundary conditions are deduced, and the nonexistence of periodic traveling waves is also obtained. Numerical simulations are carried out to support the theoretical results.