Stability ‎a‎nalysis of the transmission dynamics of an HBV model

‎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_۰. ‎if R_۰<۱, ‎the disease-free equilibrium is globally asymptotically stable by using approach that given by Kamgang and Sallet‎. ‎Then the authors prove that if R_۰>۱, ‎the disease-free equilibrium is unstable and the disease is uniformly persistent‎. ‎Furthermore‎, ‎If R_۰>۱, ‎the unique endemic equilibrium is globally asymptotically stable by using a generalization of the Poincar e-Bendixson ‎criterion.‎

Keywords:

Hepatitis B virus (HBV) , Basic reproduction number (R_۰) , ‎G‎ompound matrices , Global ‎stability.‎