Influenza dynamics are additionally complicated by considerable antigenic diversity in human influenza viruses. Within each of the two influenza A subtypes (H3N2 and H1N1) co-circulating prior to 2009, continual evolution selecting for antigenic novelty was seen [8] . The dynamics of intra-subtype evolution is characterized by relatively stable strains periodically replaced by antigenically distinct types in punctuated evolution events [8] [9] [10] . In addition, there is evidence of immune-mediated competition between subtypes [10] . These mechanisms combine to generate complex seasonal behaviour, featuring a range of annual attack rates (AARs) and epidemic durations and alternating sequences of dominant annual subtypes and strains [11] . Detailed and computationally intensive simulations are required to fully integrate the epidemiological and genetic aspects of long-term behaviour [10, 12] . However, strain-specific data with sufficient temporal resolution to fit such a model are not available. We therefore adopt a simplified description here and model two weakly interacting subtypes, with evolution within each subtype being represented by a gradual loss of immunity of the previously exposed host population, a so-called SIRS (susceptible-infected-recoveredsusceptible) model. While use of SIRS models to represent intra-subtype evolution is not uncommon [13] [14] [15] , previous models of influenza time series have not accounted for dynamics generated by multiple interacting subtypes.