Taking account of spatial heterogeneity, latency in infected individuals, and time for shed bacteria to the aquatic environment, we build a delayed nonlocal reaction-diffusion cholera model. A feature of this model is that the incidences are of general nonlinear forms. By using the theories of monotone dynamical systems and uniform persistence, we obtain a threshold dynamics determined by the basic reproduction number $ \mathcal {R}_0 $. Roughly speaking, the cholera will die out if $ \mathcal{R}_0<1 $ while it persists if $ \mathcal{R}_0>1 $. Moreover, we derive the explicit formulae of $ \mathcal{R}_0 $ for two concrete situations.

中文翻译：

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延迟非局部反应扩散霍乱模型的阈值动力学

考虑到空间异质性，感染个体的潜伏期以及细菌散发到水生环境的时间，我们建立了延迟的非局部反应扩散霍乱模型。该模型的一个特点是，入射具有一般的非线性形式。通过使用单调动力学系统和一致持久性的理论，我们获得了由基本再现数$ \ mathcal {R} _0 $决定的阈值动力学。粗略地说，如果$ \ mathcal {R} _0 <1 $，则霍乱将消失，而如果$ \ mathcal {R} _0> 1 $，霍乱将持续存在。此外，我们导出了针对两种具体情况的$ \ mathcal {R} _0 $的显式公式。