Traveling waves in nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay.

This paper studies the traveling waves in a nonlocal dispersal SIR epidemic model with nonlinear incidence and distributed latent delay. It is found that the traveling waves connecting the disease-free equilibrium with endemic equilibrium are determined by the basic reproduction number R 0 and the minimal wave speed c ∗ . When R 0 > 1 and c > c ∗ , the existence of traveling waves is established by using the upper-lower solutions, auxiliary system, constructing the solution map, and then the fixed point theorem, limiting argument, diagonal extraction method, and Lyapunov functions. When R 0 > 1 and 0 < c < c ∗ , the nonexistence result is also obtained by using the reduction to absurdity and the theory of asymptotic spreading. [ABSTRACT FROM AUTHOR]