Optimal Control with Singular Solution for SIR Epidemic Systems

Mathematical modeling represents a useful instrument to study the evolution of an epidemic spread and to determine the best control strategy to reduce the number of infected subjects. The computation of the singular solution for a SIR epidemic system with vaccination control is performed; a constructive algorithm for the computation of a bang-singular-bang optimal solution is proposed and, for the specific choice of the parameters typical for a SIR model, the two switching instants, as well as the singular profile, are determined. Numerical simulations are reported to show the results of the described procedure.