Mathematical modeling in epidemiology and phage-bacteria systems with an emphasis on spatial models /by Wei Wei.

The research presented in this dissertation centers on the role of spatial structure in the population dynamics of pathogens. We employed several types of mathematical models to address two specific topics: (1) the fate of mutant pathogens in a spatially expanding epidemic; (2) the spatio-temporal dynamics of two virus populations competing for a common (bacterial) host in the presence of several levels of spatial structure. Ultimately, these issues form a foundation for discussions of pathogen evolution.;In the first project, we studied the dynamics of mutant pathogens arising in an epidemic initiated by a wild-type pathogen in a population of susceptible hosts. We used three types of mathematical models (ordinary differential equations, reaction-diffusion equations, and interacting particle systems) to determine the mechanisms responsible for the success or failure of a mutant strain in both well-mixed and spatially structured environments. We found that transmission rate, virulence, mutation rate and spatial configuration affect the fate of mutants in both spatial and well-mixed settings although the relative importance of these factors can differ greatly in these two settings. Since evolutionary dynamics are grounded in the fate of mutants that happen to arise, these factors also play an important role in the evolution of virulence.;In the second project, we investigated effects of spatial structure on bacteriophage competition. We used competition experiments, interacting particle system models and associated computer simulations to test the hypothesis that spatial structure and host evolution facilitate coexistence of two competing species with limited resources even though one of the species appears to be dominant.Thesis (Ph. D., Bioinformatics and Computational Biology)--University of Idaho, May 2008