Dynamics analysis in a tumor-immune system with chemotherapy

An ordinary differential equation (ODE) model of tumor growth with the effect of tumor-immune interaction and chemotherapeutic drug is presented and studied. By analyzing the existence and stability of equilibrium points, the dynamic behavior of the system is discussed elaborately. The chaotic dynamics can be obtained in our model by equilibria analysis, which show the existence of chaos by calculating the Lyapunov exponents and the Lyapunov dimension of the system. Moreover, the action of the infusion rate of the chemotherapeutic drug on the resulting dynamics is investigated, which suggests that the application of chemotherapeutic drug can effectively control tumor growth. However, in the case of high-dose chemotherapeutic drug, chemotherapy-induced effector immune cells damage seriously, which may cause treatment failure.