作者:王晶囡，刘胜男，臧璐，王化娣
Authors:WANG Jing-nan,LIU Sheng-nan,ZANG Lu ,WANG Hua-di摘要:摘要:为了研究树突细胞辅助T细胞抗肿瘤的动力学性质，根据树突细胞与T细胞杀伤肿瘤的机制，建立树突细胞辅助T细胞抗肿瘤模型。以输注活性T 细胞增加率为参数，给出了无肿瘤平衡点和肿瘤正平衡点的存在条件。利用规范型与中心流形理论，得到模型的规范型、解的稳定条件与周期解的存在条件。用Matlab数值模拟展示系统出现无肿瘤现象与肿瘤周期增长现象。在相同参数条件下，比较不同初值和不同T 细胞的激活量逐渐增加时，肿瘤复发的时间间隔与疗效的差异。理论结果与数值结果揭示了树突细胞辅助T细胞抑制肿瘤生长的一些特有规律。
Abstract:Abstract: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.

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