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

Optimal Control of a SIR Epidemic With ICU Constraints and Target Objectives