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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 R 0 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. [ABSTRACT FROM AUTHOR]

This paper investigates the traveling wave in a nonlocal dispersal susceptible-infected-removed epidemic model with general nonlinear incidence and nonlocal delayed effects. It is shown that the existence and nonexistence of nontrivial traveling waves are fully determined by the basic reproduction number R 0 and critical wave speed c*. When R 0 > 1 and c > c*, the existence of traveling waves is obtained by means of an auxiliary system, the methods of upper-lower solutions, Schauder's fixed point theorem, and some limiting techniques. When R 0 > 1 and 0 < c < c*, the nonexistence of traveling waves is established by the reduction to absurdity and the theory of asymptotic spreading. [ABSTRACT FROM AUTHOR]