In this paper, we consider the monotone travelling wave solutions of a reaction–diffusion epidemic system with nonlocal delays. We obtain the existence of monotone travelling wave solutions by applying abstract existence results. By transforming the nonlocal delayed system to a non-delayed system and choosing suitable small positive constants to define a pair of new upper and lower solutions, we use the contraction technique to prove the asymptotic stability (up to translation) of monotone travelling waves. Furthermore, the uniqueness and Lyapunov stability of monotone travelling wave solutions will be established with the help of the upper and lower solution method and the exponential asymptotic stability.

中文翻译：

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非局部延迟反应-扩散流行系统中双稳态波前的存在与稳定性

在本文中，我们考虑了具有非局部延迟的反应-扩散流行系统的单调行波解。我们通过应用抽象存在结果来获得单调行波解的存在性。通过将非局部延迟系统转换为非延迟系统并选择合适的小正常数来定义一对新的上下解，我们使用收缩技术证明了单调行波的渐近稳定性（直到平移）。此外，将借助上下解法和指数渐近稳定性建立单调行波解的唯一性和李雅普诺夫稳定性。