In this paper, we propose a non-autonomous and diffusive SIR epidemic model based on the fact that the infection rate, the removal rate and the death rate often vary in time. The explicit formulas of the basic reproduction number [Formula: see text] and the minimum wave speed [Formula: see text] are derived. Applying upper-lower solution method and Schauder’s fixed point theorem, we show that when [Formula: see text], [Formula: see text] and the diffusion rates satisfy a certain condition, a time periodic traveling wave solution exists in the model. By the method of contradiction analysis and the comparison arguments together with the properties of the spreading speed of an associated subsystem, we prove that when [Formula: see text] and [Formula: see text] or [Formula: see text] and [Formula: see text], the model possesses no time periodic traveling wave solutions.

中文翻译：

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三分量非自治和反应扩散流行病模型中的时间周期行波

在本文中，我们基于感染率、清除率和死亡率经常随时间变化的事实，提出了一种非自主和扩散的 SIR 流行病模型。推导出基本再生数[公式：见正文]和最小波速[公式：见正文]的显式公式。应用上下解法和Schauder不动点定理，证明当[公式：见正文]、[公式：见正文]且扩散速率满足一定条件时，模型中存在时间周期行波解。通过矛盾分析的方法和比较论据以及关联子系统的传播速度的性质，我们证明当[公式：见文本]和[公式：见文本]或[公式：见文本]和[公式: 见正文],