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The maths behind coexistence through connectivity

By Laith Yakob

Mathematical models have evolved with our understanding of antimicrobial resistance, yielding important insight into the origin, spread and control of pathogens with reduced susceptibility to drug treatments. However, one critical shortcoming of models to date is that they are not particularly permissive to the long-term coexistence of drug-sensitive and drug-resistant pathogenic strains; eventually, based on a battle between selection pressures and fitness costs associated with resistance, one strain endures victorious. However, this measures up poorly to the reality of the situation: whether it’s MRSA in the USA or aminopenicillins in Europe, long-term coexistence of resistant and susceptible strains seems a widely applicable feature of AMR.

new study from Harvard University sheds light on what may be the reason for this mismatch between models and data. Starting with a very basic mathematical description of the competition between susceptible and resistant pathogen strains for their resources (i.e., you and me), the authors iteratively increase model complexity, eventually resulting in a meta-population: a system of connected sub-populations. How is this different to previous models? Well, most previous models can be envisaged as being just one of these sub-populations, with inhabiting individuals randomly contacting each other.

This meta-population model is then interrogated through a series of analyses to show some true-to-life key features of AMR. Namely, that coexistence is a robust result (i.e. is not contingent on very particular “cherry-picked” parameter values); and, that large differences in resistance levels are possible even between connected regions with similar antibiotic consumption rates (e.g. carbapenems resistance in Kpneumoniae in Italy has dwarfed levels in neighbouring countries for years).

Population structure is by no means the only mechanism through which coexistence can come about. Other biologically plausible causes include superinfection and within-population heterogeneities in pathogen transmission and/or host recovery rates. The take home, then, is that this is not the new ‘best’ explanation for why we see both drug-susceptible and -resistant pathogenic strains persisting among populations for many years; just, one further explanation. Likely, there is not a single, correct answer to everything, always. These theories do not necessarily competitively exclude each other. There is room for coexistence.

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