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

Pierre-Alexandre Bliman (1) , Michel Duprez (2, 3)

1 MAMBA - Modelling and Analysis for Medical and Biological Applications
2 MIMESIS - Computational Anatomy and Simulation for Medicine
3 ICube - Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie

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 essays showing the best possible performance for a large set of basic reproduction numbers and lockdown durations and intensities.

Mots clés: Herd immunity; SIR model; Attack ratio; Non-pharmaceutical interventions; Optimal control

Domaines: Optimisation et contrôle [math.OC]

Pierre-Alexandre Bliman, Michel Duprez. How Best Can Finite-Time Social Distancing Reduce Epidemic Final Size?. Journal of Theoretical Biology, 2021, 511, pp.110557. ⟨10.1016/j.jtbi.2020.110557⟩. ⟨hal-02953047v2⟩