To explore the influence of environmental pollution on the spread of waterborne diseases, we formulate a diffusive waterborne pathogen model with the distinct diffusion rates and spatial heterogeneity. We define the basic reproduction number $R_0$ and show its threshold role: if $R_0<1,$ the disease-free steady state is globally asymptotically stable; if $R_0>1,$ the model system is uniformly persistent. The asymptotic profiles of the endemic steady state are discussed when the diffusion rates of the susceptible populations approach zero.

中文翻译：

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环境污染对水生病原体模型的影响：全局动力学和渐近曲线

为了探索环境污染对水传播疾病传播的影响，我们建立了具有明显扩散率和空间异质性的水传播病原体模型。我们定义基本的复制编号${\mathrm{[R}}_0$ 并显示其阈值作用：如果 ${\mathrm{[R}}_0<\mathrm{1个}，$无病稳态是全局渐近稳定的；如果${\mathrm{[R}}_0>\mathrm{1个}，$模型系统具有统一的持久性。当易感种群的扩散率接近零时，讨论了地方性稳态的渐近曲线。