Acquired immunodeficiency syndrome (AIDS) has rapidly emerged as one of the main global health problems. It is a widely accepted fact that HIV causes AIDS, a condition in which the normal human immune system becomes suppressed, rendering the affected individual unable to fight serious or fatal infections. Infection by HIV-1 has many unusual quantitative features. An example is the average 10-year lag from the start of infection till HIV totally dominates the immune system. In recent decades, the infection caused by HIV which leads to AIDS has been the subject of many researches. Although many progresses have happened in understanding different aspects of virus-host interaction, mechanisms through which HIV causes AIDS are still under question. Nowadays, mathematical modeling has become an integral part of the research on the HIV infection. Elaborate mathematical models cannot only help further understanding of HIV dynamics ,but also provide useful predictions that can be used as the basis for assessing the effects of chemotherapy or immunotherapy and for the design of optimum therapies and effective vaccines. The time scale to develop a specific immune response may vary from days to weeks. In the case of HIV, the entire course of infection involves two different time scales. The primary infection exhibits the same characteristics as any other viral infection: a dramatic increase of the virus population during the first 2–6 weeks, followed by a sharp decline, due to the action of the immune system. However, instead of being completely eliminated after the primary infection, as many other viruses, a low HIV concentration is detected for a long asymptomatic time: the clinical latency period. This period may vary from one to ten years. Besides the low virus burden detected during this period, a gradual deterioration of the immune system is manifested by the reduction of CD4+T-cell populations in the peripheral blood. The third phase of the disease is achieved when the concentration of the T cells is lower than a critical value, leading to the development of AIDS. So, in this research, first, basic concepts of immunology and virology are explained. After that the structure and history of HIV virus which is the aim of this project is discussed. Then the simplest model of dynamic and demography is studied. In following steps, quasispecies model, some concepts of Evoluionary Games, Prisoner’s Dilemma game and tit-for-tat strategy and cellular automata model which is a discontinuous model in time and space are introduced and investigated, respectively. Finally, the results obtained applying above models to HIV virus are discussed.The goal of this thesis is to use a combination of cellular automata and quasispecies model in order to investigate the dynamic interaction which produces AIDS between HIV viruses and immune system. Changing virus concentration, applying cellular and homoral immune separately and removing the RNA mutation of viruses, are studied. Additionally, throughout changing the length of Antigen epitope on virus variable, a threshold for genetic variety that immune system can bear until the infection caused by HIV doesn't lead to AIDS, is obtained.