Capturing Bacterial Ecology in models of antibiotic treatments

Understanding how bacteria react to antibiotic challenge is key in optimising treatments. Bacteria grow in an ever-changing environment, where growth is limited by competition for space and/or resources. But bacteria can also cross-protect or help each other, for instance by absorbing or degrading antibiotics. When faced with treatment, a denser population may thus be able to tolerate a higher dose. Upon lysis, bacteria cells can also release nutrients that will be recycled for others. These multiple potentially counteracting factors highlight the need for mathematical models to understand the effects of these ecological interactions. From simple to complex formulations, even in ODE systems, there are many modelling choices one can make depending on the processes of interest. Here we aim at a clear overview of the different modelling approaches available and what they mean biologically. We recognise a lack of extended mathematical analysis in the literature and aim to develop a more thorough understanding of model behaviours through equilibrium and stability analysis. Ultimately, we aim to understand how ecological forces of both competition and cooperation affect bacterial population response to antibiotics and probability of resistance emergence.