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

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