Optimal epidemic suppression under an ICU constraint

Abstract

By acting on the transmission rate of an infectious disease through various measures, which with we are all familiar today, it is possible to control the epidemic so that the health system is not overwhelmed. Such policies have an economic cost, assumed to be (semi-)linear with respect to the modification of the sociability factor. Making furthermore the hypothesis that the evolution of the infectious disease is driven by a time-inhomogeneous version of the S.I.R. equations, we will describe the optimal policy, present the proof and consider future extensions. It is a joint work with Daniel Spiro (Uppsala University) and Jörgen Weibull (Stockholm School of Economics).