On the stability analysis and optimal vaccination control of some SEIR type epidemic diseases mathematical model

In this thesis, the mathematical modelling and stability of some SEIR-type epidemic diseases is studied. Furthermore, through the vaccination 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, SEIR dynamical system is introduced, the stability of the model is analyzed and the obtained numerical solutions of the system are interpreted. In the third chapter, a control system is constructed by adding a control parameter which characterizes the vaccination control on SEIR dynamical system. An optimal control problem is introduced for the control system and the solution is obtained. In the fourth chapter, an algorithm for the numerical solution of the optimal control problem is presented and numerical solutions are interpreted through the graphical representations.