This paper is mainly concerned with the exponential stability and uniqueness of traveling waves of a delayed nonlocal dispersal SIR epidemic model. We first prove the stability of traveling waves by using the weighted energy method, where the traveling waves are allowed to be non-monotone. Next we establish the exact asymptotic behavior of traveling waves at-8 by using Ikehara's theorem. Then the uniqueness of traveling waves is obtained by the stability result. Finally, we discuss how the nonlocal dispersal affects the stability of traveling waves. The conclusion shows that the nonlocal dispersal slows down the convergence rate of the solution to the traveling waves.

中文翻译：

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非局部扩散SIR流行病模型行波的稳定性和唯一性

本文主要关注延迟非局部扩散 SIR 流行模型行波的指数稳定性和唯一性。我们首先使用加权能量法证明行波的稳定性，其中允许行波是非单调的。接下来，我们使用 Ikehara 定理建立行波在 8 处的精确渐近行为。然后由稳定性结果得到行波的唯一性。最后，我们讨论了非局部扩散如何影响行波的稳定性。结论表明，非局部扩散减慢了行波解的收敛速度。