Subthreshold coexistence of strains: the impact of vaccination and mutation.

We consider a model for a disease with two competing strains and vaccination. The vaccine provides complete protection against one of the strains (strain 2) but only partial protection against the other (strain 1). The partial protection leads to existence of subthreshold equilibria of strain 1. If the first strain mutates into the second, there are subthreshold coexistence equilibria when both vaccine-dependent reproduction numbers are below one. Thus, a vaccine that is specific toward the second strain and that, in absence of other strains, should be able to eliminate the second strain by reducing its reproduction number below one, cannot do so because it provides only partial protection to another strain that mutates into the second strain.