Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects
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 eq...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017036 |
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| author | Blessing O. Emerenini Stefanie Sonner Hermann J. Eberl |
| author_facet | Blessing O. Emerenini Stefanie Sonner Hermann J. Eberl |
| author_sort | Blessing O. Emerenini |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1dc243357cf748b9a3ca38e27aa6192c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-1dc243357cf748b9a3ca38e27aa6192c2025-01-24T02:39:47ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-05-0114362565310.3934/mbe.2017036Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effectsBlessing O. Emerenini0Stefanie Sonner1Hermann J. Eberl2Biomedical Physics, Dept. Physics, Ryerson University, 350 Victoria Street Toronto, ON, M5B 2K3, CanadaInstitute for Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36,8010 Graz, AustriaDept. Mathematics and Statistics, University of Guelph, 50 Stone Road East, ON, N1G 2W1, CanadaWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2017036quorum sensingbiofilmcell dispersaldensity dependent diffusionexistenceuniquenessnumerical simulation |
| spellingShingle | Blessing O. Emerenini Stefanie Sonner Hermann J. Eberl Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects Mathematical Biosciences and Engineering quorum sensing biofilm cell dispersal density dependent diffusion existence uniqueness numerical simulation |
| title | Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects |
| title_full | Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects |
| title_fullStr | Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects |
| title_full_unstemmed | Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects |
| title_short | Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects |
| title_sort | mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects |
| topic | quorum sensing biofilm cell dispersal density dependent diffusion existence uniqueness numerical simulation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017036 |
| work_keys_str_mv | AT blessingoemerenini mathematicalanalysisofaquorumsensinginducedbiofilmdispersalmodelandnumericalsimulationofhollowingeffects AT stefaniesonner mathematicalanalysisofaquorumsensinginducedbiofilmdispersalmodelandnumericalsimulationofhollowingeffects AT hermannjeberl mathematicalanalysisofaquorumsensinginducedbiofilmdispersalmodelandnumericalsimulationofhollowingeffects |