Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth - WANG Jingnan; LU Lanfen; YANG Dezhong; ZHANG Yanqiao (Journal of Harbin University of Science and Technology)
In order to investigate the effect of T cells on inhibiting the tumor growth, based on the limitation of T cell immune recognition，we construct a T cell immune saturation recognition model with time delay Using the transformation rate, the attack rate of T cells, and the activation time delay as three main parameters, the existence and stability conditions of nontumor equilibrium and positive equilibrium point of tumors are obtained Though the theories of norm form and the central manifold, we obtain the norm form of this model, the critical conditions of undergoing Hopf bifurcation and the properties of the Hopf bifurcation Matlab numerical simulations are performed to show the phenomena of notumor and tumor periodic solution of the system At the same time, we compare the difference of the critical value of time delay between the model with saturated function and the model with bilinear function when the model undergoes Hopf bifurcation under the same conditions Some theoretical methods for T cells inhibiting the growth of tumors are revealed