A continuum multi-species bacterial growth model with a novel interaction scheme

Biofilms are complex structures which are inhabited by numerous amount of different species of microorganisms. Due to their ubiquity, they influence human life on an everyday basis. It is therefore important to understand the interactions between different bacterial populations within a biofilm and their reactions to outside conditions. For this purpose, mathematical models and in silico experiments have proven themselves to be fundamental. In combination with in vitro and in vivo experiments, they can give more insights and focus researchers' attention, reducing costs in the process. In this work, a comprehensive multi-species continuum-based model for the development of bacterial populations is presented. This model is capable of replicating a variety of different bacteria interactions with an arbitrary number of species, while still being comprehensive to encourage usage by researchers less familiar with mathematical modeling. In addition to a nutrient source, antibiotic agents and their effect on the biofilm can also be depicted. The model is derived using Hamilton's principle of stationary action, ensuring thermodynamic consistency automatically. The numerical examples demonstrate the model's capability to qualitatively reproduce complex interaction patterns.