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 R0and establish a threshold type result on its gl...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 R0and establish a threshold type result on its global dynamics in terms of R0,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.展开更多
基金supported by the NSFC(12161079)the XSTP(KC2023058)。
文摘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 R0and establish a threshold type result on its global dynamics in terms of R0,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.
