具时滞肿瘤T细胞免疫系统Hopf分支及肿瘤抑制

Hopf Bifurcation of Delayed Tumor-T Cell Immune System and Inhibition of Tumor Growth

为了探讨T细胞对肿瘤生长的抑制作用,根据T细胞免疫识别的有限性,建立了T细胞免疫具有饱和识别肿瘤的时滞模型。以T细胞的转换率,攻击率和效应激活时滞为参数,给出了无肿瘤平衡点和肿瘤正平衡点的存在条件与稳定条件。利用规范型与中心流形理论,得到了模型的规范型、经历Hopf分支临界条件和分支性质。再用Matlab数值模拟展示了系统出现无肿瘤与肿瘤周期增长现象。在相同环境下,比较了饱和函数模型与双线性函数模型经历Hopf分支时,效应激活时滞临界值的差异。理论分析结果揭示了T细胞在抑制肿瘤生长过程中一些理论途径。

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 non-tumor 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.