Systematic comparison of coexistence in models of drug-sensitive and drug-resistant pathogen strains

A number of mathematical models have recently been proposed to explain empirical trends of pathogen diversity. In particular, long-term coexistence of both drug-sensitive and drug-resistant variants of a single pathogen is something of a mystery, given that simple models of pathogens competing for the same ecological niche predict competitive exclusion, and more complex models admitting coexistence require assumptions that may not be justified. Coinfection is among the candidate mechanisms to generate coexistence, as it occurs in many pathogens and provides the opportunity for strains to interact directly. Recently, coinfection and competitive release have been described as creating a form of negative frequency-dependent selection that promotes coexistence, and a range of models containing coinfection have been proposed as having generic stable coexistence of multiple strains. This abundance of new models presents the challenge of comparison and interpretation. To this end, we describe a dimensionless quantity that can be used to compare the amount of coexistence generated by different models. We focus on models that include coinfection, although this framework could be generalized to a larger class of structured models.