OPTIMAL EPIDEMIC CONTROL BY SOCIAL DISTANCING AND VACCINATION OF AN INFECTION STRUCTURED BY TIME SINCE INFECTION: THE COVID-19 CASE STUDY

Motivated by the issue of COVID-19 mitigation, in this work we tackle the general problem of optimally controlling an epidemic outbreak of a communicable disease structured by age since exposure, with the aid of two types of control instruments, namely social distancing and vaccination by a vaccine at least partly effective in protecting from infection. By our analyses we could prove the existence of (at least) one optimal control pair. We derived first-order necessary conditions for optimality and proved some useful properties of such optimal solutions. Our general model can be specialized to include a number of subcases relevant for epidemics like COVID-19, such as, e.g., the arrival of vaccines in a second stage of the epidemic, and vaccine rationing, making social distancing the only optimizable instrument. A worked example provides a number of further insights on the relationships between key control and epidemic parameters.