Fifth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2003, pp. 123-142.

A transient density-dependent diffusion-reaction model for the limitation of antibiotic penetration in biofilms

Hermann J. Eberl & Messoud A. Efendiev

A mathematical model is presented that describes the disinfection of microbial biofilms by antibiotics. It is the first multi-species/multi-substrate generalization of a continuous prototype biofilm model comprising degenerating as well as fast diffusion. The boundedness of the model solution is established. The dynamic model behaviour in dependence of model parameters is studied by numerical simulations. A characteristic dimensionless parameter, the disinfection number, is derived, allowing an a priori statement whether all active biomass will be removed or not.

Published February 28, 2003.
Subject classifications: 92D25, 92C50, 35K65.
Key words: Biofilms, antibiotic disinfection, simulation, nonlinear diffusion-reaction.

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Hermann J. Eberl
Institute of Biomathematics and Biometry
GSF - National Research Centre for Environment and Health
Pf. 1129, D-85758 Neuherberg, Germany
Dept. Mathematics and Statistics, University of Guelph
Guelph, On, N1G2W1, Canada
e-mail: and
fon: +1(519) 824 4120 ext. 52622
Messoud A. Efendiev
Institute of Mathematics A
University of Stuttgart
Pfaffenwaldring 57, D-70569 Stuttgart, Germany

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