Review of mathematical models for biofilms

In this paper, we briefly review the progress made in the mathematical modeling of biofilms over the last 30 years. Biofilms constitute a spectrum of dynamical microorganisms, whose interaction with the surrounding environment and thereby induced dynamics dictates the complex properties of the living organism. Modeling of biofilms began with a low dimensional continuum description first based on kinematics and translational diffusions; later, more sophisticated microscopic dynamical mechanisms are introduced leading to the anomalous diffusion and dissipation encountered by various components in biofilms. Recently, biofilm and bulk fluid (or solvent) coupling has been investigated using discrete-continuum, multifluid and single fluid multicomponent models to treat the entire biofilm-bulk-fluid system either as a system consisting of various components whose dynamics exhibits different time scale or as a whole. We classify the models into roughly four classes: low-dimensional continuum models, diffusion limited aggregation models, continuum-discrete models, and fully coupled biofilm-fluid models. We will address some hybrid models that combine the ideas from the above categories and new computational protocols combining the existing computational tools for cell dynamics coupled with the discrete-continuum biofilm model.