Global stability and optimal control of some epidemic disease models

This thesis consists of five chapters. In the first chapter, the description of some epidemic disease models and the fundamental studies on these models in the literature are given. In the second chapter, some fundamental definitions and theorems used in the next chapters are presented. In the third chapter, we investigate the results given in the papers (Korobeinikov ve Wake, 2002), (O'Regan et al., 2010) and (Jia et al., 2018) on global stability of epidemic diseases models when the total population is constant. Numerical simulations of asymptotic stability of these epidemic disease models have been established. In the fourth chapter, we investigate the results given in the papers (Vargas De-Leon et al., 2009) and (Yusuf ve Benyah, 2012) on global stability of epidemic diseases models when the total population is not constant. Numerical simulations of asymptotic stability of these epidemic disease models have been established. In the fifth chapter, we investigate the results given in the paper (Chen et al., 2014) on global stability and optimal control of epidemic disease network model incorporating two controls which are vaccination and treatment.