  We introduce and analyze coupled, multi-strain epidemic models designed to
simulate the emergence and dissemination of mutant (e.g. drug-resistant)
pathogen strains. In particular, we investigate the mathematical and biological
properties of a general class of multi-strain epidemic models in which the
infectious compartments of each strain are coupled together in a general
manner. We derive explicit expressions for the basic reproduction number of
each strain and highlight their importance in regulating the system dynamics
(e.g. the potential for an epidemic outbreak) and the existence of nonnegative
endemic solutions. Importantly, we find that the basic reproduction number of
each strain is independent of the mutation rates between the strains --- even
under quite general assumptions for the form of the infectious compartment
coupling. Moreover, we verify that the coupling term promotes strain
coexistence (as an extension of the competitive exclusion principle) and
demonstrate that the strain with the greatest reproductive capacity is not
necessarily the most prevalent. Finally, we briefly discuss the implications of
our results for public health policy and planning.
