Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects
Blessing O. Emerenini Stefanie Sonner Hermann J. Eberl

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.

keywords: Quorum sensing biofilm cell dispersal density dependent diffusion existence uniqueness numerical simulation

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