We represent the generation time for the pathogen by an Erlang distribution with shape parameter k ¼ 4 and mean 1/a, where a ¼ 2.7 days [20, 23] . Our model incorporates two strains of influenza, for instance, representing H1N1 and H3N2, to try and capture aspects of the co-circulation of multiple influenza types and subtypes [11] . There are four immune states for individuals in the model; entirely susceptible, immune to either strain 1 or 2 and immune to both strains. The formulation allows for the inclusion of a basic cross-immunity mechanism, whereby an individual infected with either strain has a probability, f, of becoming immune to the other as well (assuming that this was not already the case) The flow between different immune states is illustrated in the electronic supplementary material. We note that this cross-immunity response is different from the shortterm non-specific response with regard to influenza strains considered elsewhere [10] , though cross-immunity is assumed to wane at the same rate as strain-specific immunity.