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We derive an exact upper bound on the epidemic overshoot for theKermack-McKendrick SIR model. This maximal overshoot value of 0.2984... occursat $R_0^*$ = 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 inManaus, Brazil highlights the public health hazard posed by overshoot forepidemics with $R_0$ near 2. Using the general analysis framework presentedwithin, we then consider more complex SIR models that incorporate vaccination.

Fundamental Bound on Epidemic Overshoot in the SIR Model