A Mathematical Model of Biofilm Growth on Degradable Substratum

We derive a mathematical model for biofilm growth on a degradable substratum. The starting point is the one-dimensional Wanner-Gujer biofilm model. The processes included are diffusion of a dissolved growth controlling substrate into the biofilm, cell lysis, detachment of biomass, and growth from substrate conversion and substratum degradation. The resulting model is a system of two non-linear ordinary differential equations, the evaluation of the right-hand side of which requires the solution of a semi-linear two-point boundary value problem. We perform standard analysis from the existence and uniqueness of solutions to equilibrium and stability analysis. Finally, we study our model through numerical simulations and investigate how biofilms evolve on degradable substratum. We find in our setting that the addition of substratum degradation has no effect on the long-term behaviour of the biofilm, but does affect the transient behaviour.