Global stability analysis for a tick-borne model
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Date
2019-05-06
Authors
Koptleuova, Daiana
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Science and Technology
Abstract
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.
Description
Submitted to the Department of Mathematics on May 6, 2019, in partial fulfillment of the
requirements for the degree of Master of Science in Applied Mathematics
Keywords
Research Subject Categories::MATHEMATICS::Applied mathematics, SIR, SIS, SIRS, epidemiological model, global asymptotic stability, Lyapunov functions, Lyapunov–LaSalle technique, endemic equilibrium states of models