The Dynamic Character Of Tumor Immnue System Research

Tumor seriously endangering the health of human beings, people have been exploring a variety of ways to conquer cancer, and construct model to study the reaction between tumor cells and immune cells has important clinical significance.With the rapid development of oncology, immunology and molecular biology, mathematics and other related disciplines, the research of tumor immunotherapy has been further developed.In this paper, we mainly consider the simplifies tumor immune model proposed by scholars Kuznetsov et al. Because of the conjunction and disjunction of effector cells and tumor cells needs some time, so we consider time delay factor in the model,first through the method of characteristic equation analysis the stability of the equilibrium point of tumor immune system. Secondly, research the existence conditions of the Hopf bifurcation and further analysis of the Hopf bifurcation, Hopf bifurcation properties of system. Finally, combined with the theoretical analysis,carried out the numerical simulation by using mathematical software Matlab, depict the tumor cells, the effect of cell waveform and phase diagram respectively. The simulation results verify the theoretical conclusions obtained before.