DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1731-1750.

DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE

刘丽雅^1,2, 蒋达清^2,3, Tasawar HAYAT^3,4, Bashir AHMAD³

1 School of Petroleum Engineering, China University of Petroleum, Qingdao 266580, China;
2 College of Science, China University of Petroleum, Qingdao 266580, China;
3 Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi Arabia;
4 Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

收稿日期:2017-08-29 修回日期:2018-04-23 出版日期:2018-12-25 发布日期:2018-12-28
通讯作者: Daqing JIANG E-mail:daqingjiang2010@hotmail.com
作者简介:Liya LIU,E-mail:liuliya 1993@hotmail.com;Tasawar HAYAT,E-mail:tahaksag@yahoo.com;Bashir AHMAD,E-mail:bashir qau@yahoo.com
基金资助:
The research of Jiang was supported by NSFC (11371085), the Fundamental Research Funds for the Central Universities (15CX08011A).

DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE

Liya LIU^1,2, Daqing JIANG^2,3, Tasawar HAYAT^3,4, Bashir AHMAD³

1 School of Petroleum Engineering, China University of Petroleum, Qingdao 266580, China;
2 College of Science, China University of Petroleum, Qingdao 266580, China;
3 Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi Arabia;
4 Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan

Received:2017-08-29 Revised:2018-04-23 Online:2018-12-25 Published:2018-12-28
Contact: Daqing JIANG E-mail:daqingjiang2010@hotmail.com
Supported by:
The research of Jiang was supported by NSFC (11371085), the Fundamental Research Funds for the Central Universities (15CX08011A).

摘要/Abstract

摘要： In this article, we present a hepatitis B epidemic model with saturated incidence. The dynamic behaviors of the deterministic and stochastic system are studied. To this end, we first establish the local and global stability conditions of the equilibrium of the deterministic model. Second, by constructing suitable stochastic Lyapunov functions, the sufficient conditions for the existence of ergodic stationary distribution as well as extinction of hepatitis B are obtained.

关键词: hepatitis B model, Lyapunov function, stability, stationary distribution, extinction

Abstract: In this article, we present a hepatitis B epidemic model with saturated incidence. The dynamic behaviors of the deterministic and stochastic system are studied. To this end, we first establish the local and global stability conditions of the equilibrium of the deterministic model. Second, by constructing suitable stochastic Lyapunov functions, the sufficient conditions for the existence of ergodic stationary distribution as well as extinction of hepatitis B are obtained.

Key words: hepatitis B model, Lyapunov function, stability, stationary distribution, extinction

刘丽雅, 蒋达清, Tasawar HAYAT, Bashir AHMAD. DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE[J]. 数学物理学报(英文版), 2018, 38(6): 1731-1750.

Liya LIU, Daqing JIANG, Tasawar HAYAT, Bashir AHMAD. DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE[J]. Acta mathematica scientia,Series B, 2018, 38(6): 1731-1750.

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DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE

DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE

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