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

doi:10.1007/s10473-024-0607-z

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (6): 2165-2189.doi: 10.1007/s10473-024-0607-z

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

Shun ZHI^1,2, Youhui SU^1,†, Hongtao NIU¹, Lizhong QIANG³

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

收稿日期:2023-10-17 修回日期:2024-07-16 发布日期:2024-12-06
通讯作者: † Youhui SU, E-mail: suyh02@163.com
作者简介:Shun ZHI, E-mail: zhishun1998@163.com;Hongtao NIU, E-mail:aniuht@163.com; Lizhong QIANG, E-mail: qianglzh@nwnu.edu.cn
基金资助:
NSFC (12161079) and the XSTP (KC2023058).

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

Shun ZHI^1,2, Youhui SU^1,†, Hongtao NIU¹, Lizhong QIANG³

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

Received:2023-10-17 Revised:2024-07-16 Published:2024-12-06
Contact: † Youhui SU, E-mail: suyh02@163.com
About author:Shun ZHI, E-mail: zhishun1998@163.com;Hongtao NIU, E-mail:aniuht@163.com; Lizhong QIANG, E-mail: qianglzh@nwnu.edu.cn
Supported by:
NSFC (12161079) and the XSTP (KC2023058).

摘要/Abstract

摘要： 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.

关键词: waterborne pathogen, environmental pollution, the basic reproduction number, seasonality

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

中图分类号:

35K57

Shun ZHI, Youhui SU, Hongtao NIU, Lizhong QIANG. THE THRESHOLD DYNAMICS OF A WATERBORNE PATHOGEN MODEL WITH SEASONALITY IN A POLLUTED ENVIRONMENT[J]. 数学物理学报(英文版), 2024, 44(6): 2165-2189.

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

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

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