Optimal Lockdown to Manage an Epidemic

TL;DR

This paper develops a unified optimal control framework to determine lockdown policies that balance epidemic control and economic impact, tailored for different country contexts.

Contribution

It introduces a novel integrated model combining epidemic dynamics and economic factors to optimize lockdown strategies.

Findings

Optimal lockdown policies vary across countries.

Economic and health trade-offs are quantitatively analyzed.

Model parameters influence lockdown effectiveness.

Abstract

We formulate an optimal control problem to determine the lockdown policy to curb an epidemic where other control measures are not available yet. We present a unified framework to model the epidemic and economy that allows us to study the effect of lockdown on both of them together. The objective function considers cost of deaths and infections during the epidemic, as well as economic losses due to reduced interactions due to lockdown. We tune the parameters of our model for Covid-19 epidemic and the economies of Burundi, India, and the United States (the low, medium and high income countries). We study the optimal lockdown policies and effect of system parameters for all of these countries. Our framework and results are useful for policymakers to design optimal lockdown strategies that account for both epidemic related infections and deaths, and economic losses due to lockdown.