MATHEMATICAL MODELING ON THE INTERACTION BETWEEN TUMOR AND THE IMMUNE SYSTEM

Abstract

In this thesis a mathematical model is presented that describes growth, immune escape and treatment of tumors. The model consists of a system of non-linear ordinary differential equations describing tumor cells and immune effectors, as well as the immune-stimulatory and suppressive cytokines IL-2 and TGF-  . In this research work, we design a mathematical model in which we want to investigate the effect of parameters on the model. Again we also investigate the existence, positivity, boundedness of the solutions and stability of the equilibrium points and evaluate the conditions at which the tumor cells will occur and persist using the parameters whether the disease becomes persistent or die out depending on the basic parameters of the model.