Minimal Wave Speed of a Nonlocal Diffusive Epidemic Model with Temporal Delay

This note is concerned with a nonlocal version of the man-environment-man epidemic model in which the dispersion of infectious agents is assumed to follow a nonlocal diffusion law modeled by a convolution operator. The purpose of this note is to show that the minimal wave speeds of properly re-scaled nonlocal diffusion equations can approximate the corresponding one of the classical diffusion equation for this model. As a byproduct, our results indicate that the temporal delay in an epidemic model can reduce the speed of epidemic spread while the nonlocal effect can increase the speed.