Yeleussinova, MeruyertKashkynbayev, ArdakTourassis, Vassilios D.2019-08-292019-08-292019-05-03http://nur.nu.edu.kz/handle/123456789/4194Submitted to the Department of Mathematics on May 3, 2019, in partial fulfillment of the requirements for the degree of Master of Science in Applied MathematicsThis 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.enAttribution-NonCommercial-ShareAlike 3.0 United StatesResearch Subject Categories::MATHEMATICS::Applied mathematicsSIRSepidemic modelpulse vaccinationPoincare mapMaster's thesis