Pathogen evolution poses a significant challenge to public health, as efforts to control the spread of infectious diseases struggle to keep up with a shifting target. To better understand this adaptive process, we turn to mathematical modelling. Specifically, we use multi-type branching processes to describe a pathogen's stochastic spread among members of a host population or growth within a single host. In each case, there is potential for new pathogen strains with different characteristics to arise through mutation.
We first develop a specific model to study the emergence of a newly introduced infectious disease, where the pathogen must adapt to its new host or face extinction in this population. In an extension of previous models, we separate the processes of host-to-host contacts and disease transmission, in order to consider each of their contributions in isolation. We also allow for an arbitrary distribution of host contacts and arbitrary mutational pathways/rates among strains. This framework enables us to assess the impact of these various factors on the chance that the process develops into a large-scale epidemic. We obtain some intriguing results when interpreted in a biological context.
Secondly, motivated by a desire to investigate the time course of pathogen evolutionary processes more closely, we derive some novel theoretical results for multi-type branching processes. Specifically, we obtain equations for: (1) the distribution of waiting time for a particular type to arise; and (2) the distribution of population numbers over time, conditioned on a particular type not having yet appeared. A few numerical examples scratch the surface of potential applications for these results, which we hope to develop further. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2010-07-28 11:43:22.984
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OKQ.1974/5947 |
| Date | 28 July 2010 |
| Creators | Alexander, Helen |
| Contributors | Queen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.)) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner. |
| Relation | Canadian theses |
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