Stability ‎a‎nalysis of the transmission dynamics of an HBV model

ýHepatitis B virus (HBV) infection is a major public health problem in the world todayý. ýA mathematical model is formulated to describe the spread of hepatitis Bý, ýwhich can be controlled by vaccination as well as treatmentý. ýWe study the dynamical behavior of the system with fixed control for both vaccination and treatmentý. ýThe results shows that the dynamics of the model is completely determined by the basic reproductive number R_0. ýif R_01, ýthe disease-free equilibrium is unstable and the disease is uniformly persistentý. ýFurthermoreý, ýIf R_0>1, ýthe unique endemic equilibrium is globally asymptotically stable by using a generalization of the Poincar e-Bendixson ýcriterion.ý