Dynamics of a reaction–diffusion waterborne pathogen model with free boundaries

Abstract

In this paper, we consider a reaction–diffusion waterborne pathogen model with free boundary. We first prove that this problem has a unique global solution, and then we show that its longtime behavior is determined by a spreading–vanishing dichotomy. Moreover, we obtain sharp criteria for spreading and vanishing, which is very different from the results in Zhou et al. (2018) that the epidemic will spread for the basic reproduction number is larger than 1.