In this paper, we propose and study an almost periodic reaction–diffusion epidemic model in which disease latency, spatial heterogeneity and general seasonal fluctuations are incorporated. The model is given by a spatially nonlocal reaction–diffusion system with a fixed time delay. We first characterise the upper Lyapunov exponent λ* for a class of almost periodic reaction–diffusion equations with a fixed time delay and provide a numerical method to compute it. On this basis, the global threshold dynamics of this model is established in terms of λ* It is shown that the disease-free almost periodic solution is globally attractive if λ* < 0, while the disease is persistent if λ* > 0. By virtue of numerical simulations, we investigate the effects of diffusion rate, incubation period and spatial heterogeneity on disease transmission.

中文翻译：

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几乎周期性环境中具有潜伏期的反应-扩散流行病模型

在本文中，我们提出并研究了一种几乎周期性的反应-扩散流行病模型，其中结合了疾病潜伏期、空间异质性和一般季节性波动。该模型由具有固定时间延迟的空间非局部反应扩散系统给出。我们首先描述了一类具有固定时间延迟的几乎周期性的反应扩散方程的上 Lyapunov 指数 λ*，并提供了一种数值方法来计算它。在此基础上，建立了该模型的全局阈值动态 λ* 表明，如果 λ* < 0，则无病几乎周期解具有全局吸引力，而如果 λ* > 0，则疾病是持续存在的。通过凭借数值模拟，我们研究了扩散速率、潜伏期和空间异质性对疾病传播的影响。