The authors propose a mathematical model to describe how a good bacterial biofilm controls the growth of a harmful pathogenic biofilm. This model is a multi-species generalization of a single-species probiotic biofilm control model, established by the same authors in a previous published paper. The underlying mechanism is a modification of the local protonated acid concentration, which in turn decreases the local pH and makes growth conditions for the patogens less favorable, while the control-agent itself is more tolerant to these changes.
The mathematical model consists of a system of five density-dependent diffusion-reaction equations including two nonlinear diffusion effects: porous medium degeneracy and fast diffusion. Completing the model with Dirichlet boundary conditions and initial conditions, and using standard techniques, the authors show existence of solutions to the model in the sense of distributions, but any result on uniqueness neither nonuniqueness is provided in the paper.
The paper ends with a numerical analysis of the model that shows that patogens are eradicated first in the deeper layers of the biofilm, close to the substratum, whereas in traditional antibiotic biofilm control, the cells in the outer layers are deactivated first.