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

摘要

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 $mathcal{R}_{0}$ and the minimal wave speed $c^{*}$ . When $mathcal{R}_{0}1$ and $cc^{*}$ , 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 $mathcal{R}_{0}1$ and $0 c c^{*}$ , the nonexistence result is also obtained by using the reduction to absurdity and the theory of asymptotic spreading.