We consider a simple model for the immune system
in which virus are able to undergo mutations and are in competition
with leukocytes. These mutations are related to several other concepts which have
been proposed in the literature like those of shape or of
virulence – a continuous notion. For a given species, the system admits a
globally attractive critical point. We prove that mutations do not affect this
picture for small perturbations and under strong structural assumptions.
Based on numerical and theoretical arguments, we also examine how,
releasing these assumptions, the system can blow-up.