In this paper, we propose a non-autonomous reaction–diffusion SIR infectious disease model with nonlinear incidence, taking fully into account the effects of periodic environmental factors as well as population dynamics on disease transmission in space, and investigate the existence of periodic traveling wave solutions satisfying boundary conditions. Specifically, we first define the basic reproductive number ${\mathcal{R}}_0$ and critical wave speed $c^{\ast }$, which will directly determine the existence of periodic traveling waves. Then, by considering a truncation problem and using fixed-point theorem, some estimation and limit techniques, the sufficient conditions on the existence of periodic traveling waves satisfying some boundary conditions are deduced for every wave speed $c>c^{\ast }$ when ${\mathcal{R}}_0>1$, and the nonexistence of periodic traveling waves is also obtained for any $c>0$ when ${\mathcal{R}}_0<1$. Finally, some numerical examples are given to verify the theoretical results.

在本文中，我们提出了一种具有非线性发病率的非自主反应-扩散SIR传染病模型，充分考虑了周期性环境因素以及人口动态对空间疾病传播的影响，并研究了周期性行波的存在。满足边界条件的解。具体来说，我们首先定义基本再生数${\mathcal{R}}_0$和临界波速$C^{*}$，这将直接确定周期性行波的存在。然后，通过考虑截断问题，利用不动点定理、估计和极限技术，推导出每个波速满足一定边界条件的周期性行波存在的充分条件。$C>C^{*}$什么时候${\mathcal{R}}_0>1$, 并且对于任何一个也不存在周期性行波$C>0$什么时候${\mathcal{R}}_0<1$. 最后，给出了一些数值例子来验证理论结果。