The analysis of a disease-free equilibrium of Hepatitis B model - Reza Akbari; Ali Vahidian Kamyad; Ali akbar Heydari; Aghileh Heydari (Sahand Communications in Mathematical Analysis, 2016)
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 $R_01$, the disease-free equilibrium is unstable and the disease is uniformly persistent.