  We introduce and discuss a minimal individual-based model for influenza
dynamics. The model takes into account the effects of specific immunization
against viral strains, but also infectivity randomness and the presence of a
short-lived strain transcending immunity recently suggested in the literature.
We show by simulations that the resulting model exhibits substitution of viral
strains along the years, but that their divergence remains bounded. We also
show that dropping any of these features results in a drastically different
behavior, leading either to the extinction of the disease, to the proliferation
of the viral strains, or to their divergence.
