@article { author = {Akbari, Reza and Vahidian Kamyad, Ali and Heydari, Ali akbar and Heydari, Aghileh}, title = {The analysis of a disease-free equilibrium of Hepatitis B model}, journal = {Sahand Communications in Mathematical Analysis}, volume = {03}, number = {2}, pages = {1-11}, year = {2016}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {}, abstract = {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.}, keywords = {Hepatitis B virus (HBV),Basic reproduction number ($R_0$),Compound matrices,Disease-Free equilibrium state,Global stability}, url = {https://scma.maragheh.ac.ir/article_19749.html}, eprint = {https://scma.maragheh.ac.ir/article_19749_d6277da45d18a2b9e2617791b8dbcc92.pdf} }