Cancer is one of the most dangerous diseases in the current era, which is the leading cause of human’s death in the world. Cancer is a group of diseases involving abnormal cell growth that have the potential to invade or spread to the other parts of human body. The role of the immune system in the tumor development covers the concept of cancer immunoediting, which includes three phases: elimination, equilibrium, and escape. The first step in controlling and treatment of a disease is cognition the disease and its behavior. The progression of the disease must be determined precisely. Game theory is a strong tool for modeling situations in which the payoffs of different entities with different strategies are depend on the action chosen by the others. Evolutionary stable strategy (ESS) is a known topic in game theory which provides a suitable tool for modeling evolution of cancer as well as the invasion of immune system. We propose and analyze three models for cancer-immune cells interactions, as follows: i) An evolutionary game model of cancer-immune interaction. ii) An evolutionary game model of proliferating, quiescent and immune cells interactions. iii) An evolutionary game model of proliferating and quiescent cells interactions. In these models, population dynamics and interactions between the immune system and cancer cells has been investigated and equilibrium points have been calculated. Stability of these equilibria or critical points have been analyzed by using of the algebraic analysis. Results show that our analyses are consistent with the reality of the cancer. At the end of the study, we investigate a therapeutic strategy based immunotherapy, certain threshold values for the frequency and applied doses are derived from our analysis. Keywords: Evolutionary game theory, Replicator dynamic, Cancer–immune interactions.
