Our model also includes a mechanism for loss of immunity, returning individuals to a susceptible state. Surveillance data show that human influenza strains can be grouped into clusters within each of which there is a high level of cross-immunity, but between which cross-immunity is much lower [8] . The appearance of a new cluster therefore corresponds to a step change in the susceptibility of the population to the current strain. Our model caricatures this process with a timescale, D, for resistant individuals to become susceptible to the current strain again. As antigenically distinct clusters appear every 2 -8 years [8, 24] , this is our expected range for values of D. There is evidence from contact studies and from modelling of influenza epidemics that infectious contact between individuals is highly assortative and agedependent, with the highest rates among school-age children [16, 25, 26] . We include these effects by stratifying the population into children (less than or equal to 14 years) and adults (more than 14 years) and employing a mixing matrix to describe contact between the two groups. The degree of assortativity is controlled by the parameter, u, and can be varied between random mixing (u ¼ 0), where groups contact each other proportional to the fraction of the population they represent, and wholly assortative (u ¼ 1) where each group mixes only with itself. Differences in intensity of contact are captured by relative susceptibility and infectiousness parameters, r and c (see the electronic supplementary material for details).