An optimal feedback control that minimizes the epidemic peak in the SIR model under a budget constraint

We give the explicit solution of optimal control problem which consists in minimizing epidemic peak SIR model when is an attenuation factor infectious rate, subject to a L1 constraint on represents budget constraint. The strategy given as feedback singular arc maintaining infected population at constant level until immunity threshold reached, and no intervention outside arc. discuss compare this with one that minimizes fixing duration single intervention, already proposed literature. Numerical simulations illustrate benefits control.