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

Optimal control for virus spreading for an SIR model