Travelling waves of nonlocal isotropic and anisotropic diffusive epidemic models with temporal delay

Abstract

This paper is concerned with a nonlocal version of the man-environment-man epidemic model in which the dispersion of the infectious agents is assumed to follow a nonlocal diffusion law modelled by a convolution operator with symmetric or asymmetric kernel. By constructing appropriate upper and lower solutions, we prove the existence of travelling wave fronts of this model. Moreover, we show that the minimal wave speed exists in this model with symmetric or asymmetric dispersion kernel, and the temporal delay in epidemic model can reduce the speed of epidemic spread.