In order to investigate the dynamical properties that effector T cells assisted by dendritic cells inhibit small-benign tumor

we establish an anti-tumor model with effector T-cells and dendritic-cells

employing the mechanism of killing tumor cells of dendritic cells and T cells.Taking the injection addition rate of activated T cells as the parameter

we obtain the existence and stability conditions of non-tumor equilibrium and tumor equilibrium.By using the theories of norm form and central manifold

we obtain the norm form of the model

as well as stability conditions and periodicity conditions of solutions.Matlab numerical simulations are performed to show the states of non-tumor equilibrium and the cycle growth of tumor in the model.Under the same parameters

the difference in the time interval between tumor recurrence and the effects of treatments is compared when the activation amount of T cells increases gradually and the initial value of the model changes.The theoretical analysis results reveal some special rules in which effector T cells assisted by dendritic cells inhibit the growth of tumors.