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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 . 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 withR0near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.
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Upper bounds on overshoot in SIR models with nonlinear incidence
Abstract We expand the calculation of the upper bound on epidemic overshoot in SIR models to account for nonlinear incidence. We lay out the general procedure and restrictions to perform the calculation analytically for nonlinear functions in the number of susceptibles. We demonstrate the procedure by working through several examples and also numerically study what happens to the upper bound on overshoot when nonlinear incidence manifests in the form of epidemic dynamics over a contact network. We find that both steeper incidence terms and larger contact heterogeneity can increase the range of communicable diseases at which the overshoot remains a relatively large public health hazard.
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- Award ID(s):
- 2327711
- PAR ID:
- 10529457
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Complexity
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 2731-8753
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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