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 journalArticlepeer-review

1 Scopus citations


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 languageEnglish (US)
Article number20230322
JournalJournal of the Royal Society Interface
Issue number209
StatePublished - Dec 6 2023

All Science Journal Classification (ASJC) codes

  • Bioengineering
  • Biophysics
  • Biochemistry
  • Biotechnology
  • Biomedical Engineering
  • Biomaterials


  • SIR model
  • epidemiology
  • overshoot


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