Optimal control for virus spreading for an SIR model

In this paper, an SIR epidemic model with variable size of population is considered. We study optimal control problem for an SIR model with "vaccination" and "treatment" as controls. It is shown that an optimal control exists. We have already used functional, that lots of researchers use, and found that this functional is not appropriate, it has a defect. Now, we fixed this defect by changing this functional. We analyze the dependence of solutions on parameter of problems and discuss our result.