Optimal control of a SIR epidemic with ICU constraints and target objectives

The aim of this paper is to provide a rigorous mathematical analysis an optimal control problem with SIR dynamics main feature our study the presence state constraints (related intensive care units ICU capacity) and strict target objectives immunity threshold). first class results provides comprehensive description different zones interest using viability tools. second achievement thorough Pontryagin extremals for aforementioned allowing obtain explicit closed-loop feedback control. All theoretical are numerically illustrated further understanding geometrical features scenarios.