How Best Can Finite-Time Social Distancing Reduce Epidemic Final Size?

TL;DR

This paper determines the optimal finite-time social distancing strategy to minimize the total number of infections in an SIR epidemic model, showing that maximum confinement during the longest allowed period is optimal.

Contribution

It provides a complete analytical solution for the optimal social distancing policy in the SIR model, including the timing and intensity of interventions.

Findings

Maximum confinement during the longest allowed period minimizes epidemic size.

Optimal timing is determined by a unique solution to a 1D optimization problem.

Numerical results illustrate the effectiveness across various parameters.

Abstract

Given maximal social distancing duration and intensity, how can one minimize the epidemic final size, or equivalently the total number of individuals infected during the outbreak? A complete answer to this question is provided and demonstrated here for the SIR epidemic model. In this simplified setting, the optimal solution consists in enforcing the highest confinement level during the longest allowed period, beginning at a time instant that is the unique solution to certain 1D optimization problem. Based on this result, we present numerical results showing the best possible performance for a large set of basic reproduction numbers and lockdown durations and intensities.