Computational and Mathematical Methods in Medicine
Volume 11 (2010), Issue 2, Pages 99-118
Original Article

A Mixed-Culture Model of a Probiotic Biofilm Control System

1Department of Mathematics and Statistics, University of Guelph, Guelph, ON, N1G 2W1, Canada
2Helmholtz Center Munich, German Research Center for Environment and Health, Institute of Biomathematics and Biometry, Neuherberg 85764, Germany

Received 24 June 2008; Accepted 13 January 2009

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a mathematical model and computer simulations for the control of a pathogenic biofilm by a probiotic biofilm. This is a substantial extension of a previous model of control of a pathogenic biofilm by microbial control agents that are suspended in the aqueous bulk phase (H. Khassehkhan and H.J. Eberl, Comp. Math. Meth. Med, 9(1) (2008), pp. 47–67). The mathematical model is a system of double-degenerate diffusion–reaction equations for the microbial biomass fractions probiotics, pathogens and inert bacteria, coupled with convection–diffusion–reaction equations for two growth controlling substrates, protonated lactic acids and hydrogen ions (pH). The latter are produced by the bacteria and become detrimental at high concentrations. In simulation studies, we find that the site of attachment of probiotics in the flow channel is crucial for success and efficacy of the probiotic control mechanism.