title: Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects.
abstract: 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.
authors.affiliation: Biomedical Physics, Dept. Physics, Ryerson University, 350 Victoria Street Toronto, ON, M5B 2K3, Canada. email: bemeren@ryerson.ca.
authors.forename: Blessing O
authors.initials: BO
authors.lastname: Emerenini
authors.forename: Stefanie
authors.initials: S
authors.lastname: Sonner
authors.forename: Hermann J
authors.initials: HJ
authors.lastname: Eberl
mesh_terms: D018441:Biofilms; D018533:Biomass; D003198:Computer Simulation; D008954:Models, Biological; D053038:Quorum Sensing