Dynamic Analysis On A Few Types Of Tumor Immune Response

As the fourth category of tumor chemotherapy treatment,Immune therapy has been received more and more attentions in recent years. The pivotal of immunotherapy is tumor immune responses, in which immune cells play a role in the premise that it must be activated by themselves or the cytokine IL-2. In order to study the mechanism of tumor immune responses in depth, two types of tumor immune therapy differential equation models are established.This paper is composed of three chapters.Firstly, the background of dynamics model is briefly reviewed. Then,we simply introduced the main work in this paper.Secondly, dealed with a model describing the interaction between tumor and immune cells. Considering the activation process and conversion of T-cells are not instantaneous but followed by some time lag, we established the three-dimensional delay differential equations to investigate dynamics of tumor immune response. By analyzing the distribution of characteristic equation root, we discussed the asymptotic stability of the equilibria of the system without delay, and studied the existence of positive equilibrium conditions. For the delay inducemodel, we have drawn the conclusions that the system is asymptoticstability of positive equilibrium and the existence conditions of Hopf bifurcation.Thirdly, we established a periodic pulse differential equation model of tumor immunotherapy by considering the periodic and transient behavior of infusing immune cells. By means of Floquet multiplier theory and comparison theorem, we got the existent conditions of the free-tumor periodic solution. Numerical simulations are carried to confirm the main theorems.