Spreading fronts in a partially degenerate integro-differential reaction–diffusion system

Abstract

This paper is concerned with the spreading and vanishing of an epidemic disease, which is described by a partially degenerate reaction–diffusion system with the nonlocal term and double free boundaries. We first consider the sign of the corresponding principal eigenvalue, which is determined by some given conditions. Then, we get the sufficient conditions that ensure the disease spreading or vanishing. At last, when spreading occurs, some rough estimates of the asymptotic spreading speed are given under some conditions.