Scheduling fixed length quarantines to minimize the total number of fatalities during an epidemic

TL;DR

This paper analyzes how to optimally schedule a fixed-length quarantine in an SIR epidemic model to minimize total fatalities, demonstrating that a single contiguous reduction in transmission rate is optimal.

Contribution

It provides a theoretical characterization of the optimal quarantine timing in an SIR model, including an integral condition for the optimal interval.

Findings

Optimal quarantine interval is a single contiguous period.

The integral condition characterizes the optimal timing.

Numerical simulations demonstrate the effectiveness of the approach.

Abstract

We consider a susceptible, infected, removed (SIR) system where the transmission rate may be temporarily reduced for a fixed amount of time. We show that in order to minimize the total number of fatalities, the transmission rate should be reduced on a single contiguous time interval, and we characterize this interval via an integral condition. We conclude with a few numerical simulations showing the actual reduction obtained.