Optimal Control of the SEIR Epidemic Model Based on Dynamical Systems Theory

We consider the susceptible-exposed-infected-removed (SEIR) epidemic
model and apply optimal control to it successfully. Here three control
inputs are considered, so that the infection rate is decreased and
exposed or infected individuals are removed. Our approach is to reduce
the computation of the optimal control input to that of the stable
manifold of an invariant manifold in a Hamiltonian system. 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 SEIR
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. Our results for the SEIR model are
very different from the previous one for the SIR model, which is
similar but simpler than the present one.