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 ${\mathcal{R}}_0>1$, there exists a critical number $c^{\ast }>0$ such that for each $c>c^{\ast }$, the system admits a nontrivial traveling wave solution with speed $c$, and for $0<c<c^{\ast }$, the system has no nontrivial traveling wave solution. When ${\mathcal{R}}_0<1$, 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 $c=c^{\ast }$ under some assumptions.

本文的主要目的是研究经处理的离散扩散SIR流行病模型的行波存在性。与Zhang和Wang（2014）的工作相比，获得了关于非平凡行波解的存在和不存在的更准确的结果。我们证明当基本繁殖数${\mathcal{[R}}_0>\mathrm{1个}$，存在一个关键数字 $C^{\ast }>0$ 这样每个 $C>C^{\ast }$，系统允许采用非平凡的行波解速度 $C$和 $0<C<C^{\ast }$，该系统没有非平凡的行波解决方案。什么时候${\mathcal{[R}}_0<\mathrm{1个}$，我们通过积分论证表明不存在非平凡的行波解。此外，根据邓和张（2020），我们得到了临界速度行波的存在。 $C=C^{\ast }$ 在某些假设下。