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

WANG Jingnan; LU Lanfen; YANG Dezhong; ZHANG Yanqiao

doi:10.15938/j.jhust.2020.02.018

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

更新时间：2026-08-31

- Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth
- Vol. 25, Issue 2, Pages: 130-137(2020)
- 作者机构：
  
  1哈尔滨理工大学理学院,哈尔滨,150080
- 作者简介：
- 基金信息：
- DOI：10.15938/j.jhust.2020.02.018
  CLC： O175;O193
- Published：2020
- 稿件说明：
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WANG Jingnan, LU Lanfen, YANG Dezhong, et al. Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth[J]. 2020, 25(2): 130-137.
DOI：

WANG Jingnan, LU Lanfen, YANG Dezhong, et al. Hopf Bifurcation of Delayed Tumor T Cell Immune System and Inhibition of Tumor Growth[J]. 2020, 25(2): 130-137. DOI： 10.15938/j.jhust.2020.02.018.

摘要

摘要: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。

Abstract

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

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Related Institution

Department of Mathematics

School of Sciences, Harbin University of Science and Technology

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