Optimal control of the SIR epidemic model based on dynamical systems theory

<p style='text-indent:20px;'>We consider the susceptible-infected-removed (SIR) epidemic model and apply optimal control to it successfully. Here two inputs are considered, so that infection rate is decreased infected individuals removed. Our approach reduce computation of input stable manifold an invariant in a Hamiltonian system. The situation which target equilibrium has center direction very different from similar previous work. Some numerical examples computer software AUTO used numerically compute given demonstrate usefulness our for SIR model. study suggests how we can decrease number quickly before critical occurs while keeping social economic burdens small.</p>