Check your assumptions: Further scrutiny of basic model frameworks of antimicrobial resistance

Since the mid-1990s, growing concerns over antimicrobial resistant (AMR) organisms has led to an increase in the use of mathematical models to explore the inter-host transmission of such infections. Previous work reviewing such models categorised them into generic frameworks based on their underlying assumptions. These assumptions dictated the coexistence between AMR and antimicrobial sensitive strains. We add to this work performing stability analyses of the frameworks, along with simulating them deterministically and stochastically. Stability analyses found that many of these assumptions lead to models having the same equilibria, but showed differences in the equilibria’s stability between models. Deterministic simulations reveal that assuming replacement of one infecting strain by another leads to an unusual antimicrobial treatment threshold. Increasing beyond this threshold causes a discontinuous increase in disease burden. The cost of AMR to pathogen fitness (lowered transmission) dictates both the threshold of treatment that causes the discontinuous increase in disease burden and the size of that increase. It was also shown that Superinfection states can be biased against resident strains and so favour coexistence of both strains. Stochastic simulations demonstrated that differing scenario starting conditions can guide models to converge upon equilibria that they may not have under deterministic simulation. These findings highlight the importance of checking assumptions when modelling AMR and strain competition more widely.