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.
机构:
Northeast Normal Univ, Sch Math & Stat, Key Lab Appl Stat MOE, Changchun 130024, Jilin, Peoples R ChinaNortheast Normal Univ, Sch Math & Stat, Key Lab Appl Stat MOE, Changchun 130024, Jilin, Peoples R China
Liu, Qun
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION,
2023,
119
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Hao, Yicheng
Luo, Yantao
论文数: 0引用数: 0
h-index: 0
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Natl Univ Def Technol, Coll Sci, Changsha 410073, Peoples R China
Xinjiang Key Lab Appl Math, Urumqi 830017, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Luo, Yantao
Huang, Jianhua
论文数: 0引用数: 0
h-index: 0
机构:
Natl Univ Def Technol, Coll Sci, Changsha 410073, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Huang, Jianhua
Zhang, Long
论文数: 0引用数: 0
h-index: 0
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Xinjiang Key Lab Appl Math, Urumqi 830017, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Zhang, Long
Teng, Zhidong
论文数: 0引用数: 0
h-index: 0
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Hao, Yicheng
Luo, Yantao
论文数: 0引用数: 0
h-index: 0
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Natl Univ Def Technol, Coll Sci, Changsha 410073, Peoples R China
Xinjiang Key Lab Appl Math, Urumqi 830017, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Luo, Yantao
Huang, Jianhua
论文数: 0引用数: 0
h-index: 0
机构:
Natl Univ Def Technol, Coll Sci, Changsha 410073, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Huang, Jianhua
Zhang, Long
论文数: 0引用数: 0
h-index: 0
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Xinjiang Key Lab Appl Math, Urumqi 830017, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
Zhang, Long
Teng, Zhidong
论文数: 0引用数: 0
h-index: 0
机构:
Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R ChinaXinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Peoples R China
机构:
Northeastern Univ, Inst Syst Sci, Shenyang, Peoples R ChinaNortheastern Univ, Inst Syst Sci, Shenyang, Peoples R China
Tian, Yilin
Liu, Chao
论文数: 0引用数: 0
h-index: 0
机构:
Northeastern Univ, Inst Syst Sci, Shenyang, Peoples R China
State Key Lab Integrated Automat Proc Ind, Shenyang, Peoples R ChinaNortheastern Univ, Inst Syst Sci, Shenyang, Peoples R China
Liu, Chao
Cheung, Lora
论文数: 0引用数: 0
h-index: 0
机构:
York Univ, Dept Math & Stat, Toronto, ON, CanadaNortheastern Univ, Inst Syst Sci, Shenyang, Peoples R China