  We consider within-host virus models with more than one strain and allow
mutation between the strains. If there is no mutation, a Lyapunov function
establishes global stability of the steady state corresponding to the fittest
strain. For small perturbations this steady state persists, perhaps with small
concentrations of some or all other strains, depending on the connectivity of
the graph describing all possible mutations. Moreover, using a perturbation
result due to Smith and Waltman, we show that this steady state also preserves
global stability.
