An explicit formula for minimizing the infected peak in an SIR epidemic model when using a fixed number of complete lockdowns

Eduardo D. Sontag

doi:10.1002/rnc.5701

An explicit formula for minimizing the infected peak in an SIR epidemic model when using a fixed number of complete lockdowns

Eduardo D. Sontag

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Careful timing of nonpharmaceutical interventions such as social distancing may avoid high “second waves” of infections of COVID-19. This article asks what should be the timing of a set of K complete-lockdowns of prespecified lengths (such as two weeks) so as to minimize the peak of the infective compartment. Perhaps surprisingly, it is possible to give an explicit and easily computable rule for when each lockdown should commence. Simulations are used to show that the rule remains fairly accurate even if lockdowns are not perfect.

Original language	English (US)
Journal	International Journal of Robust and Nonlinear Control
DOIs	https://doi.org/10.1002/rnc.5701
State	Accepted/In press - 2021
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Chemical Engineering(all)
Biomedical Engineering
Aerospace Engineering
Mechanical Engineering
Industrial and Manufacturing Engineering
Electrical and Electronic Engineering

Keywords

COVID-19
SIR model
epidemics
lockdowns
mathematical epidemiology

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10.1002/rnc.5701

Cite this

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title = "An explicit formula for minimizing the infected peak in an SIR epidemic model when using a fixed number of complete lockdowns",

abstract = "Careful timing of nonpharmaceutical interventions such as social distancing may avoid high “second waves” of infections of COVID-19. This article asks what should be the timing of a set of K complete-lockdowns of prespecified lengths (such as two weeks) so as to minimize the peak of the infective compartment. Perhaps surprisingly, it is possible to give an explicit and easily computable rule for when each lockdown should commence. Simulations are used to show that the rule remains fairly accurate even if lockdowns are not perfect.",

keywords = "COVID-19, SIR model, epidemics, lockdowns, mathematical epidemiology",

author = "Sontag, {Eduardo D.}",

note = "Funding Information: We are grateful to James Greene for many discussions, and to Franco Blanchini for the suggestion of the equal‐lengths result. Parts of this work were supported by grants NSF 1849588, ONR N00014‐21‐1‐2431, and AFOSR FA9550‐21‐1‐0289. Funding Information: Air Force Office of Scientific Research, FA9550‐21‐1‐0289; National Science Foundation, 1849588; Office of Naval Research, N00014‐21‐1‐ 2431 Funding information Publisher Copyright: {\textcopyright} 2021 John Wiley & Sons, Ltd.",

year = "2021",

doi = "10.1002/rnc.5701",

language = "English (US)",

journal = "International Journal of Robust and Nonlinear Control",

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T1 - An explicit formula for minimizing the infected peak in an SIR epidemic model when using a fixed number of complete lockdowns

AU - Sontag, Eduardo D.

N1 - Funding Information: We are grateful to James Greene for many discussions, and to Franco Blanchini for the suggestion of the equal‐lengths result. Parts of this work were supported by grants NSF 1849588, ONR N00014‐21‐1‐2431, and AFOSR FA9550‐21‐1‐0289. Funding Information: Air Force Office of Scientific Research, FA9550‐21‐1‐0289; National Science Foundation, 1849588; Office of Naval Research, N00014‐21‐1‐ 2431 Funding information Publisher Copyright: © 2021 John Wiley & Sons, Ltd.

PY - 2021

Y1 - 2021

N2 - Careful timing of nonpharmaceutical interventions such as social distancing may avoid high “second waves” of infections of COVID-19. This article asks what should be the timing of a set of K complete-lockdowns of prespecified lengths (such as two weeks) so as to minimize the peak of the infective compartment. Perhaps surprisingly, it is possible to give an explicit and easily computable rule for when each lockdown should commence. Simulations are used to show that the rule remains fairly accurate even if lockdowns are not perfect.

AB - Careful timing of nonpharmaceutical interventions such as social distancing may avoid high “second waves” of infections of COVID-19. This article asks what should be the timing of a set of K complete-lockdowns of prespecified lengths (such as two weeks) so as to minimize the peak of the infective compartment. Perhaps surprisingly, it is possible to give an explicit and easily computable rule for when each lockdown should commence. Simulations are used to show that the rule remains fairly accurate even if lockdowns are not perfect.

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KW - mathematical epidemiology

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An explicit formula for minimizing the infected peak in an SIR epidemic model when using a fixed number of complete lockdowns

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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