Influence of environmental pollution to a waterborne pathogen model: Global dynamics and asymptotic profiles

Abstract

Abstract 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.