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In this paper, a mathematical model of hepatitis B virus with vaccination and treatments is studied, Stability analysis discussed and the disease-free equilibrium and endemic equilibrium points obtained, the basic reproductive number R0 determined and became the threshold for equilibrium points stability. The study showed when R0 < 1 the disease-free equilibrium point was stable, whereas R0 > 1 the virus is endemic and the endemic equilibrium point is stable. The sensitivity analysis for the parameters that could reduce the spread of hepatitis B virus is studied. Finally the numerical simulation are established by using SageMath software package to show the effect of vaccination and treatments. We found that vaccination and also treatments give an effect on value of R0. Increasing the value of the vaccine in the immunized compartment or in the suspected compartment may decrease the value of R0 which mean reduce the spread of the disease.
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