Abstract:In order to investigate the effect of T cells oninhibiting the tumor growth

based on the limitation of T cell immunerecognition，weconstruct a T cell immune saturation recognition model with time delay Usingthe transformation rate

the attack rate of T cells

and the activation timedelay as three main parameters

the existence and stability conditions ofnontumor equilibrium and positive equilibrium point of tumors are obtainedThough the theories of norm form and the central manifold

we obtain the normform of this model

the critical conditions of undergoing Hopf bifurcation andthe properties of the Hopf bifurcation Matlab numerical simulations areperformed 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 modelwith saturated function and the model with bilinear function when the modelundergoes Hopf bifurcation under the same conditions Some theoretical methodsfor T cells inhibiting the growth of tumors are revealed