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Dynamics of a hepatitis B model with saturated incidence
Authors:Liya LIU  Daqing JIANG  Tasawar HAYAT  Bashir AHMAD
Affiliation:1. School of Petroleum Engineering, China University of Petroleum, Qingdao 266580, China;2. College of Science, China University of Petroleum, Qingdao 266580, China;3. College of Science, China University of Petroleum, Qingdao 266580, China;4. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi Arabia;5. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi Arabia;6. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
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.
Keywords:hepatitis B model  Lyapunov function  stability  stationary distribution  extinction  34F05  60H10  92D25
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