A Class of Mathematical Models Describing Processes in Spatially Heterogeneous Biofilm Communities

Abstract

We present a class of deterministic continuum models for spatially heterogeneous biofilm communities. The prototype is a single-species biofilm growth model, which is formulated as a highly non-linear system of reaction-diffusion equations for the biomass density and the concentration of the growth controlling substrate. While the substrate concentration satisfies a standard semi-linear reaction-diffusion equation the equation for the biomass density comprises two non-linear diffusion effects: a porous medium-type degeneracy and super diffusion.
When further biofilm processes are taken into account equations for several substrates and multiple biomass components have to be included in the model. The structure of these multi-component extensions is essentially different from the mono-species case, since the diffusion operator forthe biomass componentsdepends on the total biomass in the system and the equations are strongly coupled. We present the prototype biofilm growth model and give an overview of its multi-component extensions. Moreover, we summarize analytical results that were obtained for these models.