Global stability of traveling wave solutions for a discrete diffusion epidemic model with nonlocal delay effects

This paper is devoted to the study of the global stability of traveling wave solutions for discrete diffusion epidemic models with nonlocal delay effects. It is easy to show that there exists a c∗ > 0 such that when the wave speed is large than or equals to c∗, the model admits an increasing traveling wave solution. By applying the approaches, such as the weighted energy method, the comparison principle and Fourier’s transform, we prove that all traveling wavefronts with speed c > min{c*, c∗}, (c* > 0), are globally stable with the exponential convergence rate t−12e−μt for some constant μ > 0.