Pulse vaccination of a time-delayed SIRS epidemic model with nonlinear incidence rate

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dc.contributor.authorYeleussinova, Meruyert
dc.contributor.editorKashkynbayev, Ardak
dc.contributor.otherTourassis, Vassilios D.
dc.date.accessioned2019-08-29T09:24:41Z
dc.date.available2019-08-29T09:24:41Z
dc.date.issued2019-05-03
dc.descriptionSubmitted to the Department of Mathematics on May 3, 2019, in partial fulfillment of the requirements for the degree of Master of Science in Applied Mathematicsen_US
dc.description.abstractThis work deals with an application of pulse vaccination for a varying size of the population of time-delayed 𝑆𝐼𝑅𝑆 epidemic model. The dynamics of the infectious disease depends on the threshold value, 𝑅0, known as the basic reproduction number. In the classical epidemic models, this value is evaluated by means of the next generation matrix. However, this method does not work for non-autonomous systems. Since we consider the pulse vaccination strategy for epidemic models our system is naturally non-autonomous. We follow the general approach to derive 𝑅0 in terms of spectral radii of Poincare maps. Further, we show the existence of an infectious-free periodic solution and its global attractiveness for 𝑅0 < 1 and the persistence of infectious disease for 𝑅0 > 1.en_US
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/4194
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.subjectSIRSen_US
dc.subjectepidemic modelen_US
dc.subjectpulse vaccinationen_US
dc.subjectPoincare mapen_US
dc.titlePulse vaccination of a time-delayed SIRS epidemic model with nonlinear incidence rateen_US
dc.typeMaster's thesisen_US
workflow.import.sourcescience

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