Study On Mechanism And Dynamics Of Immune Cells Inhibiting Tumor Growth

Immunotherapy to inhibit tumor growth is one of the research hotspots in the area of treatment and prevention of tumor growth.In this paper,we focus on studying the mechanism and dynamics of immune cells inhibiting tumors,the main contents are as follows:Firstly,a scale-free network model describing the interaction mechanism between tumors,effector cells and cytokines is established.The existence of tumor equilibrium is further discussed in the case of multiple effector cells and cytokines with or without degree correlation.According to the critical value of the existence of tumors,different immune methods are discussed,which provides theoretical reference for inhibiting or predicting the growth of tumors.Secondly,considering the time delay and the saturation recognition in the transformation process of helper T cells to cytotoxic T cells,the immune dynamic models of tumor T lymphocyte with single and double delays are established.The stability and Hopf bifurcation of the equilibrium are analyzed.Though the theories of norm form and the central manifold,we obtain the norm form and the properties of Hopf bifurcation of single delay model.Matlab numerical simulations are performed to show the theoretical results.Finally,the purpose of inhibiting cancer is achieved by injecting cytokines in vitro combined with chemotherapy when cytokines are inactivated.A model with impulsive control of tumor growth is established.By constructing the Lyapunov function and applying the Floquet multiplier theory,the conditions of positive invariance of solution and local orbits asymptotically stability of non-tumor equilibrium point are obtained,which provide a basic theoretical guidance and approaches for clinical inhibition of cancer cells.