Fundamental bound on epidemic overshoot in the SIR model

Maximilian M. Nguyen; Ari S. Freedman; Sinan A. Ozbay; Simon A. Levin

doi:10.1098/rsif.2023.0322

Fundamental bound on epidemic overshoot in the SIR model

Maximilian M. Nguyen, Ari S. Freedman, Sinan A. Ozbay, Simon A. Levin

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

1 Scopus citations

Abstract

We derive an exact upper bound on the epidemic overshoot for the Kermack-McKendrick SIR model. This maximal overshoot value of 0.2984 · · · occurs at R0∗ - =2.151⋯. In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with R 0 near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

Original language	English (US)
Article number	20230322
Journal	Journal of the Royal Society Interface
Volume	20
Issue number	209
DOIs	https://doi.org/10.1098/rsif.2023.0322
State	Published - Dec 6 2023

All Science Journal Classification (ASJC) codes

Biotechnology
Biophysics
Bioengineering
Biomaterials
Biochemistry
Biomedical Engineering

Keywords

SIR model
epidemiology
overshoot

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10.1098/rsif.2023.0322

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abstract = "We derive an exact upper bound on the epidemic overshoot for the Kermack-McKendrick SIR model. This maximal overshoot value of 0.2984 · · · occurs at R0∗ - =2.151⋯. In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with R 0 near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.",

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AU - Freedman, Ari S.

AU - Ozbay, Sinan A.

AU - Levin, Simon A.

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AB - We derive an exact upper bound on the epidemic overshoot for the Kermack-McKendrick SIR model. This maximal overshoot value of 0.2984 · · · occurs at R0∗ - =2.151⋯. In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with R 0 near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

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Fundamental bound on epidemic overshoot in the SIR model

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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