摘要：In this paper, we propose a nonlocal diffusion infectious disease model with nonlinear incidences and distributed delay to model the transmission of the epidemic. By a fixed point theorem and a limiting argument, we establish the existence of traveling wave solutions for the model. Meanwhile, we obtain the non-existence of traveling wave solutions for the model via two-sided Laplace transform. It is found that the threshold dynamics of traveling wave solutions are entirely determined by the basic reproduction number of the corresponding spatially-homogenous delayed differential system and the minimum wave speed. A typical example is given for supporting our abstract results. Moreover, the effect of the diffusive rate of the infected individuals on the minimum wave speed is discussed.
关键词：Disease model ; Nonlocal diffusion ; Fixed point theorem ; Two-sided Laplace transform
