Optimal quarantine strategies for the COVID-19 pandemic in a population with a discrete age structure

TL;DR

This paper develops an age-structured SEIRQ model to determine optimal quarantine strategies for COVID-19 in Brazil, analyzing how timing and duration of measures impact death reduction and how delays influence quarantine planning.

Contribution

It introduces a novel age-structured control model for COVID-19 quarantine optimization, considering quarantine timing, duration, and delays in implementation.

Findings

Optimal quarantine timing varies by age group.

Longer quarantine periods generally reduce deaths more.

Delays in quarantine initiation alter the optimal relaxation schedule.

Abstract

The goal of this work is to study the optimal controls for the COVID-19 epidemic in Brazil. We consider an age-structured SEIRQ model with quarantine compartment, where the controls are the quarantine entrance parameters. We then compare the optimal controls for different quarantine lengths and distribution of the total control cost by assessing their respective reductions in deaths in comparison to the same period without quarantine. The best strategy provides a calendar of when to relax the isolation measures for each age group. Finally, we analyse how a delay in the beginning of the quarantine affects this calendar by changing the initial conditions.