Traveling wave solutions in a nonlocal dispersal SIR epidemic model with nonlocal time-delay and general nonlinear incidences

Abstract

This paper investigates a nonlocal dispersal epidemic model under the multiple nonlocal distributed delays and nonlinear incidence effects. First, the minimal wave speed [Formula: see text] and the basic reproduction number [Formula: see text] are defined, which determine the existence of traveling wave solutions. Second, with the help of the upper and lower solutions, Schauder’s fixed point theorem, and limiting techniques, the traveling waves satisfying some asymptotic boundary conditions are discussed. Specifically, when [Formula: see text], for every speed [Formula: see text] there exists a traveling wave solution satisfying the boundary conditions, and there is no such traveling wave solution for any [Formula: see text] when [Formula: see text] or [Formula: see text] when [Formula: see text]. Finally, we analyze the effects of nonlocal time delay on the minimum wave speed.