Optimal control of an epidemiological sir model with vaccination and treatment

In this thesis, mathematical modeling of some SIR-type epidemics has been examined. Furthermore, through the vaccination control and treatment control added to the dynamical system, an optimal control problem is formed for the obtained control system. This thesis consists of four chapters. In the first chapter, some fundamental definitions and theorems used for the stability analysis of dynamical systems and optimal control applications are presented. In the second chapter, a control system is constructed by adding a control parameter which characterizes the vaccination and treatment control on SIR dynamical system and stability analysis is conducted. In the third chapter,An optimal control problem is introduced for the control system and the solution is obtained. In the fourth chapter, effect of optimal control on SIR model examined numerically and numerical solutions are interpreted through the graphical representations.