| Summary: | Abstract 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 $\mathcal{R}_{0}$ and the minimal wave speed c ∗ $c^{*}$ . When R 0 > 1 $\mathcal{R}_{0}>1$ and c > c ∗ $c>c^{*}$ , 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 $\mathcal{R}_{0}>1$ and 0 < c < c ∗ $0< c< c^{*}$ , the nonexistence result is also obtained by using the reduction to absurdity and the theory of asymptotic spreading.
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