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Mathematical modelling of bacterial attachment to surfaces : biofilm initiation
Thesis (MSc)--Stellenbosch University, 2011.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2011
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| _version_ | 1867614107315732480 |
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| access_status_str | Open Access |
| author | El Moustaid, Fadoua |
| author2 | Ouhinou, A. |
| author_browse | El Moustaid, Fadoua Ouhinou, A. |
| author_facet | Ouhinou, A. El Moustaid, Fadoua |
| author_sort | El Moustaid, Fadoua |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2011. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/17931 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:46:46.943Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2011 |
| publishDateRange | 2011 |
| publishDateSort | 2011 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/17931 Mathematical modelling of bacterial attachment to surfaces : biofilm initiation El Moustaid, Fadoua Ouhinou, A. Uys, L. Stellenbosch University. African Institute for Mathematical Sciences. Mathematical models Bacterial biofilms Chemotaxis Dynamical systems Dissertations -- Mathematics Theses -- Mathematics Thesis (MSc)--Stellenbosch University, 2011. ENGLISH ABSTRACT: Biofilms are aggregations of bacteria that can thrive wherever there is a watersurface or water-interface. Sometimes they can be beneficial; for example, biofilms are used in water and waste-water treatment. The filter used to remove contaminants acts as a scaffold for microbial attachment and growth. However, biofilms could have bad effects, especially on a persons health. They can cause chronic diseases and serious infections. The importance of biofilms in industrial and medical settings, is the main reason of the mathematical studies performed up to now, concerning biofilms. Biofilms have been mathematical modelling targets over the last 30 years. The complex structure and growth of biofilms make them difficult to study. Biofilm formation is a multi-stage process and occurs in even the most unlikely of environmental conditions. Models of biofilms vary from the discrete to the continuous; accounting for one-species to multi-species and from one-scale to multi-scale models. A model may even have both discrete and continuous parts. The implication of these differences is that the tools used to model biofilms differ; we present and review some of these models. The aim in this thesis is to model the early initiation of biofilm formation. This stage involves bacterial movement towards a surface and the attachment to the boundary which seeds a biofilm. We use a diffusion equation to describe a bacterial random walk and appropriate boundary conditions to model surface attachment. An analytical solution is obtained which gives the bacterial density as a function of position and time. The model is also analysed for stability. Independent of this model, we also give a reaction diffusion equation for the distribution of sensing molecules, accounting for production by the bacteria and natural degradation. The last model we present is of Keller-Segel type, which couples the dynamics of bacterial movement to that of the sensing molecules. In this case, bacteria perform a biased random walk towards the sensing molecules. The most important part of this chapter is the derivation of the boundary conditions. The adhesion of bacteria to a surface is presented by zero-Dirichlet boundary conditions, while the equation describing sensing molecules at the interface needed particular conditions to be set. Bacteria at the boundary also produce sensing molecules, which may then diffuse and degrade. In order to obtain an equation that includes all these features we assumed that mass is conserved. We conclude with a numerical simulation. AFRIKAANSE OPSOMMING: Biofilms is die samedromming van bakterieë wat kan floreer waar daar ’n wateroppervlakte of watertussenvlak is. Soms kan hulle voordelig wees, soos byvoorbeeld, biofilms word gebruik in water en afvalwater behandeling. Die filter wat gebruik word om smetstowwe te verwyder, dien as ’n steier vir mikrobiese verbinding en groei. Biofilms kan ook egter slegte gevolge he, veral op ’n persoon se gesondheid. Hulle kan slepende siektes en ernstige infeksies veroorsaak. Die belangrikheid van biofilms in industriële en mediese omgewings, is die hoof rede vir die wiskundige studies wat tot dusver uitgevoer is met betrekking tot biofilms. Biofilms is oor die afgelope 30 jaar al ’n teiken vir wiskundige modellering. Die komplekse struktuur en groei van biofilms maak dit moeilik om hul te bestudeer. Biofilm formasie is ’n multi-fase proses, en gebeur selfs in die mees onwaarskynlikste omgewings. Modelle wat biofilms beskryf wissel van die diskreet tot die kontinu, inkorporeer een of meer spesies, en strek van eentot multi-skaal modelle. ’n Model kan ook oor beide diskreet en kontinue komponente besit. Dit beteken dat die tegnieke wat gebruik word om biofilms te modelleer ook verskil. In hierdie proefskrif verskaf ons ’n oorsig van sommige van hierdie modelle. Die doel in hierdie proefskrif is om die vroeë aanvang van biofilm ontwikkeling te modeleer. Hierdie fase behels ’n bakteriële beweging na ’n oppervlak toe en die aanvanklike aanhegsel wat sal ontkiem in ’n biofilm. Ons gebruik ’n diffusievergelyking om ’n bakteriële kanslopie te beskryf, met geskikte randvoorwaardes. ’n Analities oplossing is verkry wat die bakteriële bevolkingsdigtheid beskryf as ’n funksie van tyd en posisie. Die model is ook onleed om te toets vir stabiliteit. Onafhanklik van die model, gee ons ook ’n reaksiediffusievergelyking vir die beweging van waarnemings-molekules, wat insluit produksie deur die bakterieë en natuurlike afbreking. Die laaste model wat ten toon gestel word is ’n Keller-Segel tipe model, wat die bakteriese en waarnemings-molekule dinamika koppel. In hierdie geval, neem die bakterieë ’n sydige kanslopie agter die waarnemings molekules aan. Die belangrikste deel van hierdie hoofstuk is die afleiding van die randvoorwaardes. Die klewerigheid van die bakterieë tot die oppervlak word vvorgestel deur nul-Dirichlet randvoorwaardes, terwyl die vergelyking wat waarnemingsmolekule gedrag by die koppelvlak beskryf bepaalde voorwaardes nodig het. Bakterieë op die grensvlak produseer ook waarnemings-molekules wat diffundeer en afbreek. Om te verseker dat al hierdie eienskappe omvat is in ’n vergelyking is die aanname gemaak dat massa behoud bly. Ter afsluiting is numeriese simulasie van die model gedoen. 2011-11-17T09:22:31Z 2011-12-05T13:12:28Z 2011-11-17T09:22:31Z 2011-12-05T13:12:28Z 2011-12 Thesis http://hdl.handle.net/10019.1/17931 en_ZA Stellenbosch University 54 p. : ill. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Mathematical models Bacterial biofilms Chemotaxis Dynamical systems Dissertations -- Mathematics Theses -- Mathematics El Moustaid, Fadoua Mathematical modelling of bacterial attachment to surfaces : biofilm initiation |
| title | Mathematical modelling of bacterial attachment to surfaces : biofilm initiation |
| title_full | Mathematical modelling of bacterial attachment to surfaces : biofilm initiation |
| title_fullStr | Mathematical modelling of bacterial attachment to surfaces : biofilm initiation |
| title_full_unstemmed | Mathematical modelling of bacterial attachment to surfaces : biofilm initiation |
| title_short | Mathematical modelling of bacterial attachment to surfaces : biofilm initiation |
| title_sort | mathematical modelling of bacterial attachment to surfaces biofilm initiation |
| topic | Mathematical models Bacterial biofilms Chemotaxis Dynamical systems Dissertations -- Mathematics Theses -- Mathematics |
| url | http://hdl.handle.net/10019.1/17931 |
| work_keys_str_mv | AT elmoustaidfadoua mathematicalmodellingofbacterialattachmenttosurfacesbiofilminitiation |