During the past years HIV-1 infection has been one of the most important challenges for different societies and they have been doing several efforts to control infection and to cure it. After outbreak of HIV in U.S.A in 1981 scientists tried to cure this disease; for this purpose they developed different methods. One of these methods is using mathematics to model interactions of HIV virion with T cells in body. In 1991 Rob de Boer, Heraba and Perelson modeled interactions of T cells with HIV virions. Although before them some research groups modeled the interactions, but their work was not based on very careful experiments and so was not as important as Boer, Hraba and Perelson's model. In fact, Boer, Hraba and Perelson's model is the first work that has been done with careful experiments and is valuable. After this attempt other mathematicians developed several models in order to analyze HIV interactions with body's cells. Before these models medical workers were not aware about importance of mathematics in their work; but after these models they became aware about importance of mathematics in their work and many medical hospitals used these models in their researches. One of the latest developments in this field is injecting a new virus to the body in order to control HIV infection. This method has been done in different animals and a mathematical model for this method has been proposed by Revilla and Ramos. They developed a model in which interactions of T cells in body, HIV virus and injected virus were shown. This model is simulation of HIV in some animals and in human body has not been tested. In Revilla and Ramos's work only the model has been introduced and the equilibrium points have been found. They have done some numerical simulations in their work but have not analyzed the model by using advanced mathematical tools. In this thesis some mathematical models are analyzed that have been developed for the purpose of curing HIV. First of all, a model that has been developed by Revilla and Ramos is analyzed. This part consists of the following sections: First of all, the model and its basic reproduction number is introduced. In this section, the concept of reproduction number and its benefits for analyzing models of diseases is reviewed. Also we find equilibrium points that are: infection-free, single infection and double infection. After that stability of the infection-free equilibrium is analyzed; In this part, Jacobian matrix is formed and its characteristic equation for determining sign of its roots is found. In the next section, stability analysis of the single-infection equilibrium is discussed and finally, in the last part, double infection equilibrium is analyzed. In this part we will apply Ruth-Hurwitz's criterion to understand occurrence of hopf bifurcation. Also by doing some numerical simulation all the theoretical results are verified. At the end of this thesis we will also analyzed mathematical models for HIV drug therapy which is our work and we hope to publish its results in appropriate journals.