• Author / Creator
    Thanarajah, Silogini
  • 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.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
  • Examining committee members and their departments
    • Li, Michael ( Mathematical and Statistical Sciences)
    • Van Roessel, Henry J.J. ( Mathematical and Statistical Sciences)
    • Li, Bingtuan ( Mathematics, University of Louisville)
    • De Vries, Gerda ( Mathematical and Statistical Sciences)
    • Wong, Yau Shu ( Mathematical and Statistical Sciences)