Modeling the Impact Of Environmental Factors, Diapause and Control Strategies on Tick and Tick-Borne Disease Dynamics

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dc.contributor.advisorWu, Jianhong
dc.contributor.authorTosato, Marco
dc.date.accessioned2022-12-14T16:28:35Z
dc.date.available2022-12-14T16:28:35Z
dc.date.copyright2022-07-18
dc.date.issued2022-12-14
dc.date.updated2022-12-14T16:28:35Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractIn this thesis, we focus on mathematical formulation and analyses for a specific vector responsible for a wide variety of diseases: ticks. Due to climate change, various tick species are rapidly spreading northward from the United States and have increasingly affected the Canadian population through a variety of tick-borne diseases including Lyme disease. In order to address this problem, the Public Health Agency of Canada has dedicated an entire section of its website to discuss the risks and the possibility of preventing, recognising and treating tick-bites. It is therefore important to analyse tick and tick-borne disease dynamics in order to better understand, study and prevent possible new outbreaks. We aim to achieve this by using mathematical and epidemiological tools including dynamical systems, ordinary and delay differential equations, basic reproduction numbers and Hopf bifurcation theory. For this purpose, we produce three different models to study the effect of physiological features such as diapause, control strategies and the effect of environmental conditions on tick and tick-borne disease persistence and periodicity. The first model we propose is a two-patch tick population model in which we show how the tick reproduction number $R_{T,c}$ affects the long-term behaviours of tick population and how it might lead to extinction, convergence to a coexistent or to a periodic solution. The second model is a single tick population model with switching delays. In this, we prove how oscillations of different frequencies caused by two delays might produce multi-cycle periodic solutions. The last model we analyse is a tick-host model including host control strategies. In this work, we find that there are situations in which the improper application of repellent and acaricide may lead to unexpected results and improve disease spread instead of reducing it.
dc.identifier.urihttp://hdl.handle.net/10315/40674
dc.languageen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectApplied mathematics
dc.subjectEpidemiology
dc.subject.keywordsAcaricide
dc.subject.keywordsClimate change
dc.subject.keywordsCo-feeding
dc.subject.keywordsControl methods
dc.subject.keywordsDelay differential equations
dc.subject.keywordsDiapause
dc.subject.keywordsDynamical systems
dc.subject.keywordsHopf bifurcations
dc.subject.keywordsPeriodically switching delays
dc.subject.keywordsPeriodic solutions
dc.subject.keywordsRepellent
dc.subject.keywordsSpatial models
dc.subject.keywordsTicks
dc.titleModeling the Impact Of Environmental Factors, Diapause and Control Strategies on Tick and Tick-Borne Disease Dynamics
dc.typeElectronic Thesis or Dissertation

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