(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.