Journal
MATHEMATICAL BIOSCIENCES AND ENGINEERING
Volume 14, Issue 3, Pages 625-653Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2017036
Keywords
Quorum sensing; biofilm; cell dispersal; density dependent diffusion; existence; uniqueness; numerical simulation
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Funding
- Ontario Ministry for Agriculture, Food and Rural Affairs through the HQP Scholarship program
- Natural Science and Engineering Research Council of Canada through the Discovery Grant program
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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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