Influenza A viruses exhibit complex epidemiological patterns in a number of mammalian and avian hosts. Understanding transmission of these viruses necessitates taking into account their evolution, which represents a challenge for developing mathematical models. This is because the phrasing of multi-strain systems in terms of traditional compartmental ODE models either requires simplifying assumptions to be made that overlook important evolutionary processes, or leads to complex dynamical systems that are too cumbersome to analyse.