Fundamental Bound on Epidemic Overshoot in the SIR Model

A bstract 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 . Using the general analysis framework presented within, we then consider more complex SIR models, such as those that incorporate vaccination or contact heterogeneity. We analyze models that consider vaccinations and show that the presence of vaccinated individuals decreases the maximum possible overshoot. For epidemics where the contact structure is given by a network, we numerically find that increased contact heterogeneity lowers the maximal overshoot value and weakens the dependency of overshoot on transmission.