Dynamical behavior of a stochastic epidemic model for cholera

Qun Liu; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.1016/j.jfranklin.2018.11.056

Dynamical behavior of a stochastic epidemic model for cholera

Qun Liu
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi

Northeast Normal University
King Abdulaziz University
China University of Petroleum (East China)
Quaid-I-Azam University

Research output: Contribution to journal › Review article › peer-review

35 Scopus citations

Abstract

In this paper, a stochastic epidemic model for cholera is proposed and investigated. Firstly, we establish sufficient conditions for extinction of the disease. Then we establish sufficient criteria for the existence of a unique ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The existence of an ergodic stationary distribution implies that all the individuals can be coexistent in the long run. Finally, some examples together with numerical simulations are introduced to illustrate our theoretical results.

Original language	English
Pages (from-to)	7486-7514
Number of pages	29
Journal	Journal of the Franklin Institute
Volume	356
Issue number	13
DOIs	https://doi.org/10.1016/j.jfranklin.2018.11.056
State	Published - Sep 2019
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

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10.1016/j.jfranklin.2018.11.056

Cite this

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title = "Dynamical behavior of a stochastic epidemic model for cholera",

abstract = "In this paper, a stochastic epidemic model for cholera is proposed and investigated. Firstly, we establish sufficient conditions for extinction of the disease. Then we establish sufficient criteria for the existence of a unique ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The existence of an ergodic stationary distribution implies that all the individuals can be coexistent in the long run. Finally, some examples together with numerical simulations are introduced to illustrate our theoretical results.",

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AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

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AB - In this paper, a stochastic epidemic model for cholera is proposed and investigated. Firstly, we establish sufficient conditions for extinction of the disease. Then we establish sufficient criteria for the existence of a unique ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The existence of an ergodic stationary distribution implies that all the individuals can be coexistent in the long run. Finally, some examples together with numerical simulations are introduced to illustrate our theoretical results.

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ER -

Dynamical behavior of a stochastic epidemic model for cholera

Abstract

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