Theses and Dissertations

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Browsing Theses and Dissertations by Author "Kashkynbayev, Ardak"

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    Global stability analysis for a tick-borne model
    (Nazarbayev University School of Science and Technology, 2019-05-06) Koptleuova, Daiana; Kashkynbayev, Ardak; Tourassis, Vassilios D.
    This 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.
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    Pulse vaccination of a time-delayed SIRS epidemic model with nonlinear incidence rate
    (Nazarbayev University School of Science and Technology, 2019-05-03) Yeleussinova, Meruyert; Kashkynbayev, Ardak; Tourassis, Vassilios D.
    This 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.