1Department of Mathematical Sciences, Payame Noor University ,P.O.Box 19395-3697 , Tehran ,Iran.
2Department of Mathematics Sciences , University of Ferdowsi, Mashhad, Iran.
3Research Center for Infection Control and Hand Hygiene, Mashhad University Of Medical Sciences, Mashhad, Iran.
4Department of Mathematical Sciences, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran.
Hepatitis B virus (HBV) infection is a major public health problem in the world today. A mathematical model is formulated to describe the spread of hepatitis B, which can be controlled by vaccination as well as treatment. We study the dynamical behavior of the system with fixed control for both vaccination and treatment. The results shows that the dynamics of the model is completely determined by the basic reproductive number R_0. if R_0<1, the disease-free equilibrium is globally asymptotically stable by using approach that given by Kamgang and Sallet. Then the authors prove that if R_0>1, the disease-free equilibrium is unstable and the disease is uniformly persistent. Furthermore, If R_0>1, the unique endemic equilibrium is globally asymptotically stable by using a generalization of the Poincar e-Bendixson criterion.