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Competition of Fast and Slow Movers for Renewable and Diffusive Resources, Phage-Bacteria Interactions in a Petri Dish, Competition of Motile and Immotile Bacterial Strains in a Petri Dish

Thanarajah, Silogini

Supervisor and department: Wang, Hao Mathemaical and Statistical Sciences

Examining committee member and department: Van Roessel, Henry J.J. Mathematical and Statistical Sciences Li, Michael Mathematical and Statistical Sciences Wong, Yau Shu Mathematical and Statistical Sciences Li, Bingtuan Mathematics, University of Louisville De Vries, Gerda Mathematical and Statistical Sciences

Department: Department of Mathematical and Statistical Sciences

Specialization: Applied Mathematics

Date accepted: 2013-08-23T13:23:53Z

Graduation date: 2013-11

Degree: Doctor of Philosophy

Degree level: Doctoral

Abstract: Partial differential equations PDEs have been used to model the movement of bacteria, phages, and animals. Species movement and competition exist in many interesting practical applications such as dental plaque, animal movement, and infectious diseases. This dissertation consists of three main sections: bacterial competition in a petri dish, bacteria-phage interaction in a petri dish, and animal movements. Competition of motile and immotile bacterial strains for nutrients in a homogeneous nutrient environment is dependent on the relevant bacterial movement properties. To study undirected bacterial movement in a petri dish, we modify and extend the bacterial competition model used in Wei et al. 2011 to obtain a group of more realistic PDE models. Our model suggests that in agar media the motile strain is more competitive than the immotile strain, while in liquid media both strains are equally competitive. Furthermore, we find that in agar as bacterial motility increases, the extinction time of the motile bacteria decreases without competition, but increases with competition. In addition, we show the existence of traveling-wave solutions mathematically and numerically.To study the role of bacteriophage in controlling the bacterial population, we construct a group of bacteria-phage petri dish models. We present rigorous mathematical results and obtain insightful numerical results. The analysis of these models leads to an elegant explanation of species long term behavior, patient recovery time, and the most important factors affecting the growth rate of bacteria. Our results can potentially provide some guidance for future phage therapy. Motivated by the evolution of animal movement, we study competition of fast and slow moving animals by extending our bacteria model to incorporate a resource renewal term. We use linear and nonlinear resource uptake functions to run and test simulations. Conclusions from our linear model are consistent with Lotka-Volterra type models. Interestingly, our nonlinear model exhibits two new outcomes. If we further assume the fast mover has a larger resource uptake rate than the slow mover, it is possible that the slow mover is excluded by the fast mover.

Language: English

DOI: doi:10.7939-R33J39747

Rights: Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.





Autor: Thanarajah, Silogini

Fuente: https://era.library.ualberta.ca/



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