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

  • Shun ZHI ,
  • Youhui SU ,
  • Hongtao NIU ,
  • Lizhong QIANG
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  • 1. School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221018, China;
    2. School of Science, Shenyang University of Technology, Shenyang 110870, China;
    3. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Shun ZHI, E-mail: zhishun1998@163.com;Hongtao NIU, E-mail:aniuht@163.com; Lizhong QIANG, E-mail: qianglzh@nwnu.edu.cn

Received date: 2023-10-17

  Revised date: 2024-07-16

  Online published: 2024-12-06

Supported by

NSFC (12161079) and the XSTP (KC2023058).

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.

Cite this article

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 . DOI: 10.1007/s10473-024-0607-z

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