Wave propagation in a nonlocal dispersal SIR epidemic model with nonlinear incidence and nonlocal distributed delays

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.