Numerical soluion of model on the interaction between tumor and immune system

Abstract

The Kirschner-Panetta (KP) model of cancer cell describes the interaction between tumour cells, e ector cells and interleukin{2 which are clinically utilized as medical treatment. The model selects a rich concept of immune-tumour dynamics. In This thesis, we have proposed and analyzed a nonlinear mathematical model for the study of interaction between tumor and immune system. The model is analyzed using stability theory of di erential equations. The equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the model is also performed by using fourth order Runge- Kutta method which supports the theoretical ndings. It is found that both e ector cell and tumor cells. Hence tumor load can be eliminated with time if the treatment terms increases.For certain conditions are satis ed. It is further found that the system appears to exhibit periodic limit cycles and decreases the life of tumor for some ranges of the system parameters.