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

J R Soc Interface. 2023 Dec;20(209):20230322. doi: 10.1098/rsif.2023.0322. Epub 2023 Dec 6.

Authors

Maximilian M Nguyen¹, Ari S Freedman², Sinan A Ozbay³, Simon A Levin²

Affiliations

¹ Lewis-Sigler Institute, Princeton University, Princeton, NJ 08544, USA.
² Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA.
³ Bendheim Center for Finance, Princeton University, Princeton, NJ 08544, USA.

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 [Formula: see text]. 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 R₀ near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

Keywords: SIR model; epidemiology; overshoot.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Communicable Diseases* / epidemiology
Epidemics*
Epidemiological Models
Humans
Models, Biological
Pandemics
Vaccination

Associated data

figshare/10.6084/m9.figshare. c.6935471