الفهرس 
الغلافOnly 14 pages are availabe for public view
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Abstract
There are two kinds of tumors, benign and malignant tumors. Benign tumor is not dangerous, while malignant tumor is very dangerous in human body where it destroys the human body. Cancer is a malignant tumor and is a killer disease which is one of the most causes of human death. The immune system plays the important role in the defense of the body. It tries to identify and destroy the virus causing the disease. When cancer attacks human body, the immune system resists against tumor cells and tries to eliminate them. There are many kinds of therapies with which we try to treat cancer. Immunotherapy is an important one for the treatment of cancer. It is considered a therapy by using cytokines and adoptive cellular immunotherapy. These cytokines activate lymphocytes to grow and differentiate. Therefore, immunotherapy activates and helps the immune system to fight and destroy tumor cells.
The aim of this work is to analyze two kinds of mathematical models for the inter¬action between the tumor cells and the immune system. We first consider a mathe¬matical model [39] which describes the interaction between the tumor cells and the immune system in-vivo (inside animal body). Then, we consider a mathematical model [36] which describes the interaction among the effector cells, the tumor cells and Interleukin-2 in-vitro (outside animal body). We study the effect of changing some important model-parameters on the behavior of these models. Also, we analyze the bifurcation for these models and study the tumor clearance possibility in such models. In all models we consider both a saturating and a bilinear incidence. In addition, we apply the optimal control theory [14], [19] to maximize the effects of the immunotherapy while minimizing the cost of the control.