Some mathematical modeling and analysis in epidemiology

In the first chapter of this thesis, which consists of four chapters, the literature about mathematical modeling and the position of the thesis in the literature are introduced. In the second chapter, some basic definitions and theorems related to the concepts mentioned in the thesis are presented. In the third chapter, which is the first original part of the thesis, a mathematical model including an effective vaccination strategy in the spread of epidemic diseases is created and the stabilities of the equilibrium points of the model are analyzed. In the last chapter, a model describing the spread of epidemics, which can also be transmitted through vectors, is created and some results are given regarding the stability of the disease-free equilibrium point of the model.