The threshold dynamics of a waterborne pathogen model with seasonality in a polluted environment

This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution. For this model, we derive the basic reproduction number R-0 and establish a threshold type result on its global dynamics in terms of R-0, which predicts the extinction or persistence of diseases. More precisely, the disease-free steady state is globally attractive if R-0 < 1, while the system admits at least one positive periodic solution and the disease is uniformly persistent if R-0 > 1. Moreover, we carry out some numerical simulations to illustrate the long-term behaviors of solutions and explore the influence of environmental pollution and seasonality on the spread of waterborne diseases.