Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Optimal Immunity Control and Final Size Minimization by Social Distancing for the SIR Epidemic Model

Abstract : The aim of this article is to understand how to apply partial or total containment to SIR epidemic model during a given finite time interval in order to minimize the epidemic final size, that is the cumulative number of cases infected during the complete course of an epidemic. The existence and uniqueness of an optimal strategy is proved for this infinite-horizon problem and a full characterization of the solution is provided. The best policy consists in applying the maximal allowed social distancing effort until the end of the interval, starting at a date that is not always the closest date and may be found by a simple algorithm. Both theoretical results and numerical simulations demonstrate that it leads to a significant decrease of the epidemic final size. We show that in any case the optimal intervention has to begin before the number of susceptible cases has crossed the herd immunity level, and that its limit is always smaller than this threshold. This problem is also shown to be equivalent to the minimum containment time necessary to stop at a given distance after this threshold value.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-02862922
Contributor : Yannick Privat <>
Submitted on : Sunday, January 31, 2021 - 6:59:36 PM
Last modification on : Tuesday, February 9, 2021 - 4:05:37 PM

Files

BDPV_Opt_Loc_HAL.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02862922, version 2

Citation

Pierre-Alexandre Bliman, Michel Duprez, Yannick Privat, Nicolas Vauchelet. Optimal Immunity Control and Final Size Minimization by Social Distancing for the SIR Epidemic Model. 2021. ⟨hal-02862922v2⟩

Share

Metrics

Record views

113

Files downloads

43