In this article, we present the transmission dynamics of the acute and chronic hepatitis B epidemic problem. To control the spread of hepatitis in a community, we first develop a mathematical model for the transmission of the virus of hepatitis B. After framing the mathematical model, we show the existence and uniqueness of the
solution, then mathematically analyze the model and determine the disease-free equilibrium state of the model. Besides, we determine the basic reproduction number R0 for this model which is interpreted epidemiologically. Next, we study the local stability of the diseasefree-equilibrium state and show that if ,1 R0

mathematical modeling, basic reproduction number, stability, numerical simulation, SEIR model