Chemical pesticides have long been used to control insect populations on field crops, and their widespread availability and ease of manipulation present an ideal system for the exploration of the relationship between vital rates and population dynamics. Research has shown that models of population effects of insecticides are more accurate when time-varying parameters are used, but the scientific community has been slow to accept such models, which may involve complicated mathematics such as partial differential equations. Additionally, many of the pesticides now in use have both acute and sublethal effects, and these differing modes of action, along with concerns for the scientific community's understanding of the models, motivate a new approach to mathematical modeling of the effects of insecticides on population dynamics. We first consider an ordinary differential equation model, which, while simple, provides highly accurate fits to population data, though it accounts for only one generation at a time without explicitly considering reproductive effects. An evaluation of the effects of insecticides on insect fecundity is considered separately. We then develop, implement, and analyze a coupled time-delay differential equation model, which incorporates information for multiple generations and is an intermediate model in terms of ease of understanding for non-mathematicians. Sensitivity results for the time delay kernel are also presented.
| Identifer | oai:union.ndltd.org:NCSU/oai:NCSU:etd-03262008-150916 |
| Date | 15 April 2008 |
| Creators | Joyner, Sarah Lynn |
| Contributors | Dr. H.T. Banks, Dr. Robert H. Martin, Dr. Pierre A. Gremaud |
| Publisher | NCSU |
| Source Sets | North Carolina State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://www.lib.ncsu.edu/theses/available/etd-03262008-150916/ |
| 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, dis sertation, 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 NC State University 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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