Global stability analysis for a tick-borne model

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dc.contributor.authorKoptleuova, Daiana
dc.contributor.editorKashkynbayev, Ardak
dc.contributor.otherTourassis, Vassilios D.
dc.date.accessioned2019-08-29T04:57:23Z
dc.date.available2019-08-29T04:57:23Z
dc.date.issued2019-05-06
dc.descriptionSubmitted to the Department of Mathematics on May 6, 2019, in partial fulfillment of the requirements for the degree of Master of Science in Applied Mathematicsen_US
dc.description.abstractThis thesis consider three type of epidemiological models: SIR, SIS and SIRS with nonlinear incidence rate and piecewise constant delay of generalized type. In this paper the total population size is varied with time elapse. We study the global asymptotic stability of the disease-free and endemic equilibrium states of models by constructing suitable Lyapunov functions and Lyapunov–LaSalle technique. The main contribution of this master thesis is to develop more realistic compartmental models by extending the literature of models with piecewise constant delay. The theoretical findings are illustrated through numerical simulations.en_US
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/4193
dc.language.isoenen_US
dc.publisherNazarbayev University School of Science and Technologyen_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectResearch Subject Categories::MATHEMATICS::Applied mathematicsen_US
dc.subjectSIRen_US
dc.subjectSISen_US
dc.subjectSIRSen_US
dc.subjectepidemiological modelen_US
dc.subjectglobal asymptotic stabilityen_US
dc.subjectLyapunov functionsen_US
dc.subjectLyapunov–LaSalle techniqueen_US
dc.subjectendemic equilibrium states of modelsen_US
dc.titleGlobal stability analysis for a tick-borne modelen_US
dc.typeMaster's thesisen_US
workflow.import.sourcescience

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