Summary: An SIR epidemic model with saturated incidence rate and a vaccination program is formulated, where the susceptibles are assumed to satisfy the logistic equation. The incidence term is of saturated form with the infected individuals. First, we have discussed the existence and the stability of both the disease free and endemic equilibrium. Second, the impact of vaccination in reducing \(\mathcal R(u)\) is tackled. Then, to achieve control of the disease, a control problem is formulated and it is shown that an optimal control exists for our model. The optimality system is derived and solved. Finally, numerical simulations are performed to illustrate and verify the analytical results.