Modeling, Dynamics and Optimal Control of West Nile Virus with Seasonality

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dc.contributor.advisorZhu, Huaiping
dc.creatorAbdelrazec, Ahmed Hassan Manaa
dc.date.accessioned2015-01-26T14:29:04Z
dc.date.available2015-01-26T14:29:04Z
dc.date.copyright2014-06-12
dc.date.issued2015-01-26
dc.date.updated2015-01-26T14:29:04Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractWest Nile virus (WNv) is a mosquito-borne disease which arrived in Canada in 2001. It has kept spreading across the country and still remains a threat to public health. In this dissertation, we formulate dynamical models and apply theory of dynamical systems to investigate the behavior of the transmission of WNv in the mosquito-bird cycle and humans. In the first part, we propose a system of ordinary differential equations to model the role of corvids and non-corvids birds in the transmission of WNv in the mosquito-bird cycle in a single season and proved the existence of backward bifurcation in the model. In the second part, we consider another deterministic model to study the impact of seasonal variations of the mosquito population on the transmission dynamics of WNv. We prove the existence of periodic solutions under specific conditions. As for the third part, the latter model is extended to assess the impact of some anti-WNv control measures; by re-formulating the model as an optimal control problem. For mosquito-borne diseases, it is essential to access and forcast the virus risk. Therefore in the final part, we generalize the risk index, minimum infection rate (MIR) by using a compartment model for WNv, to define a dynamical minimum infection rate (DMIR) for assessing risk of WNv. By using the data from Peel region, we test and forecast the weekly risk of WNv which can help identify the optimal mitigation strategies.
dc.identifier.urihttp://hdl.handle.net/10315/28202
dc.language.isoen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectApplied mathematics
dc.subjectEpidemiology
dc.subjectEcology
dc.subject.keywordsOptimal controlen_US
dc.subject.keywordsWest Nile virusen_US
dc.subject.keywordsMathematical modelingen_US
dc.subject.keywordsBackward bifurcationen_US
dc.subject.keywordsSeasonalityen_US
dc.titleModeling, Dynamics and Optimal Control of West Nile Virus with Seasonality
dc.typeElectronic Thesis or Dissertation

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