THE THRESHOLD DYNAMICS OF A WATERBORNE PATHOGEN MODEL WITH SEASONALITY IN A POLLUTED ENVIRONMENT

doi:10.1007/s10473-024-0607-z

Abstract

Abstract: 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 $\mathcal{R}_{0}$ and establish a threshold type result on its global dynamics in terms of $\mathcal{R}_{0}$, which predicts the extinction or persistence of diseases. More precisely, the disease-free steady state is globally attractive if $\mathcal{R}_{0}<1$, while the system admits at least one positive periodic solution and the disease is uniformly persistent if $\mathcal{R}_{0}>1$. 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.

Key words: waterborne pathogen, environmental pollution, the basic reproduction number, seasonality

CLC Number:

35K57

Shun ZHI, Youhui SU, Hongtao NIU, Lizhong QIANG. THE THRESHOLD DYNAMICS OF A WATERBORNE PATHOGEN MODEL WITH SEASONALITY IN A POLLUTED ENVIRONMENT[J].Acta mathematica scientia,Series B, 2024, 44(6): 2165-2189.

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