Optimal Control in Pandemics

TL;DR

This paper develops an optimal control strategy for balancing economic costs and infection containment during a pandemic, using a novel 'virus time' approach within the SIR model to derive effective lockdown policies.

Contribution

It introduces a mathematical framework using 'virus time' to optimize lockdown levels, minimizing economic damage while maintaining fixed health costs.

Findings

Optimal lockdown strategies derived from the model

Mathematical formulation using 'virus time'

Guidelines for controlled lockdown adjustments

Abstract

During a pandemic, there are conflicting demands arising from public health and economic cost. Lockdowns are a common way of containing infections, but they adversely affect the economy. We study the question of how to minimise the economic damage of a lockdown while still containing infections. Our analysis is based on the SIR model, which we analyse using a clock set by the virus. This use of the "virus time" permits a clean mathematical formulation of our problem. We optimise the economic cost for a fixed health cost and arrive at a strategy for navigating the pandemic. This involves adjusting the level of lockdowns in a controlled manner so as to minimise the economic cost.