Electronic Journal of Differential Equations,
Conf. 10 (2002), pp. 123-142.

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


Authors: Hermann J. Eberl (National Research Centre, Neuherberg, Germany)
Messoud A. Efendiev (Univ. of Stuttgart, Germany)
 
Abstract: 
 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 {\it a priori} statement whether all active
 biomass will be removed or not.


Published February 28, 2003.
Math Subject Classifications: 92D25, 92C50, 35K65.
Key Words: Biofilms; antibiotic disinfection; simulation; nonlinear diffusion-reaction.