Traveling waves for a discrete diffusive SIR epidemic model with treatment

Abstract

The main purpose of this paper is to study the existence of traveling waves for a discrete diffusive SIR epidemic model with treatment. Compared to the work in Zhang and Wang (2014), more accurate results about the existence and nonexistence of nontrivial traveling wave solutions are obtained. We prove that when the basic reproduction number R0>1, there exists a critical number c∗>0 such that for each c>c∗, the system admits a nontrivial traveling wave solution with speed c, and for 0<c<c∗, the system has no nontrivial traveling wave solution. When R0<1, we show that there exists no nontrivial traveling wave solution by an integration argument. In addition, based on Deng and Zhang (2020), we obtain the existence of traveling waves with the critical speed c=c∗ under some assumptions.