An epidemic model is a simplified means of describing the transmissionrnof communicable disease through individuals. In this paper the mathematicsrnbehind the model and the various tools for judging effectiveness of policiesrnand control methods on the spread of infectious diseases in populations hasrnbeen analyzed mathematically. And it has been applied to specific diseases tornstudy the propagation of diseases using the mathematical epidemic model.rnEpidemic models are many types form that select SVEIRS model and discussedrnthe dynamics and control of infectious diseases, but quantifying the underlyingrnepidemic structure can be challenging especially for new and understudiedrndiseases. SVEIRS model is that generalizes several classical deterministicrnepidemic models then apply it for Hepatitis B. Consider compartments ofrnsusceptible, vaccination, exposed, infected, and recovered humans without immunityrnand modeled the natural growth, natural death and death due to diseasernand the interactions between these populations.rnThe model has two equilibrium states namely, the disease - free and the endemicrnequilibrium points. The stability of each equilibrium point discussedrnhas been found to be stable or unstable. The basic reproduction number(R0)rnestimate the stability, with (R0 > 1) whenever the transmission rate was increasedrnor the recovery rate reduced but turned to the disease die out withrn(R0 < 1) whenever the transmission rate was reduced or the recovery rate increased.rnThe results of our sensitivity analysis showed that the most sensitive parameterrnthat controls the spread of Hepatitis B is the initial infection rate of thernsusceptible, b and d or death rate. Decreasing the value of b at the same raternas the other parameter values completely decreases the proportions of both therninfective and the exposed more effectively than any parameter value.rnConsider an optimal control problem subject to an SVEIRS Hepatitis B epidemicrnmodel with vaccination controls. Our aim is to find the best optimalrncontrol strategies to make the number of infectious individuals as small as possiblernand to keep the vaccination ratio of Hepatitis B as low as possible duringrna certain vaccination period that will minimize the cost of control. Pontryaginâ€™srnmaximum principle to characterize the optimal levels of the controls. Thernresulting optimality system is solved numerically by forward-backward sweeprnmethod. The results show that the optimal vaccination, drug and education usingrnmedia differs according to the controlled and uncontrolled individuals andrnhas a very desirable effect upon the population for reducing the number ofrninfected individuals. The effect of vaccination on transmission dynamics ofrnHepatitis B is studied. The resulting optimality system also showed that, thernuse of vaccinating at the highest possible rate to the population as early asrnpossible is essential for controlling an epidemic of the Hepatitis B disease.rnFinally model to simulate the data of Hepatitis B cases in the Ethiopia fromrn2015 and design a control strategy of the country to eliminate the epidemic forrnthe future course with optimal control theory.rnrnKeywords: SVEIRS-Model; mathematical models; vital dynamics; vaccinations;rnHB, HBV, Herd Immunity; epidemiology number, optimal control.