Schematic illustration of the simulation sequence.

As described in the Methods, the simulation is initiated by a pandemic in a naïve population. In subsequent seasons we assume that strain selection happens during the interepidemic period (annotated by a virus in the Figure, and corresponding to Fig 1B). This leads to a loss of strain-specific immunity due to antigenic drift, and accompanies a loss of immunity through population turnover, as well as through decay of cross-protective immunity. We assume that routine vaccination, whether conventional or universal, occurs just prior to each seasonal epidemic (annotated by a syringe in the Figure). The epidemic that follows is governed by the eq (1) in the main text, leading to a gain of immunity in the population (corresponding to Fig 1A)). We iterate through seasons in this way, ultimately reporting the ‘seasonal epidemic size’ as the mean epidemic size between seasons 5 and 24, and the ‘pace of antigenic evolution’ as the mean distance between successive strains during this period. Finally, we simulate a pandemic in year 25, assuming a virus to which cross-protective immunity, and not strain-matched immunity, is effective.