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

Optimal immunity control by social distancing for the SIR epidemic model

Abstract : Until a vaccine or therapy is found against the SARS-CoV-2 coronavirus, reaching herd immunity appears to be the only mid-term option. However, if the number of infected individuals decreases and eventually fades only beyond this threshold, a significant proportion of susceptible may still be infected until the epidemic is over. A containment strategy is likely the best policy in the worst case where no vaccine or therapy is found. In order to keep the number of newly infected persons to a minimum, a possible strategy is to apply strict containment measures, so that the number of susceptible individuals remains close to herd immunity. Such an action is unrealistic since containment can only last for a finite amount of time and is never total. In this article, using a classical SIR model, we determine the (partial or total) containment strategy on a given finite time interval that maximizes the number of susceptible individuals over an infinite horizon, or equivalently that minimizes the total infection burden during the curse of the epidemic. The existence and uniqueness of the optimal strategy is proved and the latter is fully characterized. If applicable in practice, such a strategy would lead theoretically to an increase by 30% of the proportion of susceptible on an infinite horizon, for a containment level corresponding to the sanitary measures put in place in France from March to May 2020. We also analyze the minimum intervention time to reach a fixed distance from herd immunity, and show the relationship with the previous problem. Simulations are provided that illustrate and validate the theoretical results.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [27 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02862922
Contributor : Yannick Privat <>
Submitted on : Tuesday, June 9, 2020 - 6:35:22 PM
Last modification on : Wednesday, September 23, 2020 - 4:31:26 AM

Files

BDPV_Opt_Loc_HAL.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02862922, version 1

Citation

Pierre-Alexandre Bliman, Michel Duprez, Yannick Privat, Nicolas Vauchelet. Optimal immunity control by social distancing for the SIR epidemic model. 2020. ⟨hal-02862922⟩

Share

Metrics

Record views

208

Files downloads

163