Feedback control of social distancing for COVID-19 via elementary formulae

TL;DR

This paper introduces a simple, robust feedback control method for social distancing during COVID-19, based on epidemic modeling and differential flatness, providing practical formulas for decision makers despite uncertainties.

Contribution

It presents elementary closed-form formulas for social distancing control using epidemic models and demonstrates a model-free feedback approach that is robust to uncertainties.

Findings

Closed-form formulas enable easy implementation of social distancing policies.

Feedback control maintains robustness despite uncertainties and model mismatches.

The approach does not require precise knowledge of the recovery rate.

Abstract

Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields ele mentary closed-form formulae for open-loop social distancing scenarios, where, for instance, the increase of the number of uninfected people may be taken into account. Those formulae might therefore be useful to decision makers. A feedback loop stemming from model-free control leads to a remarkable robustness with respect to severe uncertainties and mismatches. Although an identification procedure is presented, a good knowledge of the recovery rate is not necessary for our control strategy.