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

• 论文 • 上一篇    下一篇

DYNAMICS OF A HEPATITIS B MODEL WITH SATURATED INCIDENCE

刘丽雅1,2, 蒋达清2,3, Tasawar HAYAT3,4, Bashir AHMAD3   

  1. 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 LIU1,2, Daqing JIANG2,3, Tasawar HAYAT3,4, Bashir AHMAD3   

  1. 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: 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