Dynamical properties of a SIRI epidemic model with relapse and free boundaries

Abstract

In this paper, we study an SIRI epidemic model with relapse and free boundaries, which can describe the spreading process of diseases well. At first, the existence and uniqueness of the global solution is proven. And then we obtain some sufficient conditions for the disease spreading and vanishing. We can find an $\mathcal{R}_0$ such that the disease will vanish for $\mathcal{R}_0\leq1$, otherwise, whether the disease will spread or not is determined by the initial infected region $h_0$ and spreading capacity $\mu$ of the spreading front. Moreover, the longtime behavior of the solution is given. Finally, numerical simulations are provided to illustrate the results of the analysis.

Keywords

• relapse, epidemic model, free boundary, spreading and vanishing.