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.
In this paper we study the dynamics of Hepatitis B virus (HBV) infection under administration of a vaccine and treatment, where the disease is transmitted directly from the parents to the offspring and also through contact with infective individuals. Stability of the disease-free steady state is investigated. The basic reproductive rate, $R_0$, is derived. The results show 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 stable and the disease always dies out and if $R_0>1$, the disease-free equilibrium is unstable and the disease is uniformly persistent.
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