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Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects

1. Biomedical Physics, Dept. Physics, Ryerson University, 350 Victoria Street Toronto, ON, M5B 2K3, Canada
2. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36,8010 Graz, Austria
3. Dept. Mathematics and Statistics, University of Guelph, 50 Stone Road East, ON, N1G 2W1, Canada

We analyze a mathematical model of quorum sensing induced biofilm dispersal. It is formulated as a system of non-linear, density-dependent, diffusion-reaction equations. The governing equation for the sessile biomass comprises two non-linear diffusion effects, a degeneracy as in the porous medium equation and fast diffusion. This equation is coupled with three semi-linear diffusion-reaction equations for the concentrations of growth limiting nutrients, autoinducers, and dispersed cells. We prove the existence and uniqueness of bounded non-negative solutions of this system and study the behavior of the model in numerical simulations, where we focus on hollowing effects in established biofilms.

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