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

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.

Automated summary

In this paper, a reaction-diffusion waterborne pathogen model with free boundary is studied. The existence of a unique global solution is proved, and the longtime behavior is analyzed through a spreading-vanishing dichotomy. Sharp criteria for spreading and vanishing are obtained, which differs from the previous results by Zhou et al. (2018) stating that the epidemic will spread when the basic reproduction number is larger than 1.