In the field of mathematics we are taught to think carefully about the use of theory, how theoretical assumptions leads to the development of models and how those models subsequently interact with data. However, it is relatively rare in infection medicine that a mathematical model and its predictions impinge on the lives of patients, or are used as the basis of clinical trial design or form the basis of treatment policy. There is the opportunity that these things could eventually happen in infection medicine and there are positive signs whereby the properties of antibiotics are subject to increasingly quantitative methodologies, but many gaps remain.This talk will look at some of the quantitative oddities of the antibiotics world, like the algorithm that is used to define something called an ECOFF, a variable used in the making of treatment decisions, yet the algorithm doesn’t really converge where it is supposed to. We’ll look at the use of models in (unsuccessful?) clinical trials which predict that randomly allocating antibiotics to patients is the best strategy, despite optimal control theory making very different predictions. We’ll consider the mutant selection window hypothesis which predicts that resistance accrues at far higher dosages than it actually does.

This talk will provide several stories whereby quantitative scientists have seemingly played too small a role in the development of theoretical and data analysis techniques in the field of antibiotics and it calls for more to become involved; those opportunities do exist. For instance, we are currently applying data-driven ML-type techniques to understand whether, or not, it is rational that Europe and the USA have different recommended treatment dosages for many antibiotics, it so far appears that it is not rational given the available, often sparse, data.

In summary, mathematicians have constructed a world with strong foundations that the next generation can build upon, we need the field of antibiotics to have that kind of foundation too.

Accumulating evidence suggests that the response of bacteria to antibiotics is significantly affected by the presence of other interacting microbes. These interactions are not typically accounted for when determining pathogen sensitivity to antibiotics. Resistance and the evolutionary responses to antibiotic treatments should not be considered only a trait of an individual bacterial species but also an emergent property of the microbial community in which pathogens are embedded. Interspecies interactions can affect the responses of individual species and communities to antibiotic treatment, and ultimately alter the trajectory of resistance evolution. Here, I will present examples of how co-occurring pathogens can alter the efficacy of antibiotic treatments and the evolution of resistance within the polymicrobial setting of cystic fibrosis lung infections. Acknowledging the ecological context, i.e., the interactions that occur between pathogens and within communities, is critical in understanding the diverse outcomes of antibiotic treatments within a community setting.