%0 Journal Article
%T The analysis of a disease-free equilibrium of Hepatitis B model
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Akbari, Reza
%A Vahidian Kamyad, Ali
%A Heydari, Ali akbar
%A Heydari, Aghileh
%D 2016
%\ 06/01/2016
%V 03
%N 2
%P 1-11
%! The analysis of a disease-free equilibrium of Hepatitis B model
%K Hepatitis B virus (HBV)
%K Basic reproduction number ($R_0$)
%K Compound matrices
%K Disease-Free equilibrium state
%K Global stability
%R
%X 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.
%U http://scma.maragheh.ac.ir/article_19749_d6277da45d18a2b9e2617791b8dbcc92.pdf