Dynamical Behaviors of a Stochastic Susceptible-Infected-Treated-Recovered-Susceptible Cholera Model with Ornstein-Uhlenbeck Process

Author:

Li Shenxing1,Li Wenhe1ORCID

Affiliation:

1. School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China

Abstract

In this study, a cholera infection model with a bilinear infection rate is developed by considering the perturbation of the infection rate by the mean-reverting process. First of all, we give the existence of a globally unique positive solution for a stochastic system at an arbitrary initial value. On this basis, the sufficient condition for the model to have an ergodic stationary distribution is given by constructing proper Lyapunov functions and tight sets. This indicates in a biological sense the long-term persistence of cholera infection. Furthermore, after transforming the stochastic model to a relevant linearized system, an accurate expression for the probability density function of the stochastic model around a quasi-endemic equilibrium is derived. Subsequently, the sufficient condition to make the disease extinct is also derived. Eventually, the theoretical findings are shown by numerical simulations. Numerical simulations show the impact of regression speed and fluctuation intensity on stochastic systems.

Funder

National Natural Science Foundation of China Tianyuan Mathematical Foundation

Natural Science Foundation of Heilongjiang Province

Heilongjiang Provincial Postdoctoral Science Foundation

Northeast Petroleum University Special Research Team Project

Publisher

MDPI AG

Reference38 articles.

1. Ma, Z., Zhou, Y., and Wu, J. (2009). Modeling and Dynamics of Infectious Diseases, Higher Education Press. [1st ed.].

2. A stochastic epidemic model incorporating media coverage;Cai;Commun. Math. Sci.,2016

3. World Health Organization (WHO) (2023, February 11). Cholera-Global Situation. Available online: https://www.who.int/emergencies/disease-outbreak-news/item/2023-DON437.

4. Mathematical analysis of a cholera transmission model incorporating media coverage;Beryl;Int. J. Pure. Appl. Math.,2016

5. A mathematical model for the control of cholera in Nigeria;Fatima;Res. J. Environ. Earth Sci.,2014

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3