In this thesis, we applied local analysis tools
(eigenvalue and eigenvalue elasticity analysis, global function elasticity/sensitivity analysis), and global analysis tools (deriving the location and stability of fixed points) to both aggregate and individual-level dynamic models of infectious
diseases. We sought to use these methods to gain insight into the models and to evaluate the use of these methods to study their short-term and long-term dynamics and the influences of arameters
on the models.<p>
We found that eigenvalues are effective for understanding short-term behaviours of a nonlinear system, but less effective in providing
insights of the long-term impacts of a parameter change on its behaviours. In term of disease control, local changes of behaviours,
yielded from the changes of parameters based on eigenvalue elasticity, are able to alter behaviours in a short-term, especially
in the period of a disease outbreak. While eigenvalue elasticity analysis can be helpful for understanding the impact of parameter changes for simple aggregate models, such analyses prove unwieldy and complicated, particularly for models with large number of state variables; and easily fall prey to eigenvalue multiplicity problems
for large individual-based models, and istracting artifacts associated with small denominators. In response to these concerns, we introduced other local methods (global function
elasticity/sensitivity analyses) that capture many of the advantages of eigenvalue elasticity methods with much greater simplicity. Unfortunately, parameter changes guided by these local analysis techniques are often insufficient to alter behaviours in the longer-term, such as when system behaviours approach stable endemic
equilibria. By contrast, the global analytic tools, such as fixed point location and stability analysis, are effective for providing
insights into the global behaviours of disease spread in the long-term, as well as their dependence on parameters. Using all of
the above analysis as a toolset, we gained some possible insights into combination of local and global approaches. Choice of applying
local or global analysis tools to infectious disease models is dependent on the specific target of policy makers as well as model
type.
| Identifer | oai:union.ndltd.org:USASK/oai:usask.ca:etd-12082008-154626 |
| Date | 17 December 2008 |
| Creators | Zhang, Qian |
| Contributors | Stanley, Kevin, Spiteri, Raymond J., Osgood, Nathaniel, Grassmann, Winfried K., Willoughby, Keith |
| Publisher | University of Saskatchewan |
| Source Sets | University of Saskatchewan Library |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://library.usask.ca/theses/available/etd-12082008-154626/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Saskatchewan or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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