Optimal epidemic control by social distancing and vaccination of an infection structured by time since infection: the covid-19 case study

TL;DR

This paper develops an optimal control framework for managing COVID-19 spread using social distancing and vaccination, considering the disease's progression over time since infection, and provides theoretical insights and practical examples.

Contribution

It introduces a novel optimal control model for epidemic management that incorporates time-since-infection structure and analyzes the effects of social distancing and vaccination.

Findings

Existence of at least one optimal control solution.

Derived first-order necessary conditions for optimality.

Provided insights through a worked example on control-epidemic parameter relationships.

Abstract

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 time since exposure, by the aid of two types of control instruments namely, social distancing and vaccination by a vaccine at least partly effective in protecting from infection. Effective vaccines are assumed to be made available only in a subsequent period of the epidemic so that - in the first period - epidemic control only relies on social distancing, as it happened for the COVID-19 pandemic. 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. A worked example provides a number of further insights on the relationships between key control and epidemic parameters.