Critical immune and vaccination thresholds for determining multiple influenza epidemic waves

► Influenza pandemics occur in epidemic waves. ► We use mathematical epidemiology to develop thresholds for subsequent epidemic waves. ► We combine the thresholds with known herd immunity to predict subsequent waves. ► For the 2009 influenza pandemic, we predicted the absence of the third wave in the US. ► For the 2009 influenza pandemic, we predicted the occurrence of the second wave in England.