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| Global analysis of a class of tumor-immune system dynamics |
| HUANG Pei, LIN Xiao-lin, LI Jian-quan, SONG Xiu-chao |
1. School of Arts and Sciences, Shaanxi University of Science and Technology, Xi’an 710021, China;
2. Basic Department, Air Force Engineering University, Xi'an 710051, China |
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Abstract Based on the fact that tumor cells not only stimulate the proliferation of immune
effector cells but also have the inhibiting effect on the growth of the cells, a tumor-immune dynamical
model is described by expressing the comprehensive effect of tumor cells on immune system with a
positive or negative action rate coefficient. By investigating the global dynamics of the model, it is
found that the saddle-node bifurcation and the bistable phenomenon may occur, which implies that
that the final state of tumor development depends on the initial state, and the corresponding threshold
conditions are obtained. And the effect of the intrinsic input of effector cells and the action rate
coefficient of tumor cells on effector cells on the dynamics of the model is analyzed. The obtained
results show that the model may have complex dynamical behaviors when the inhibition effect of
tumor cells on effector cells is strong enough.
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Published: 05 July 2019
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一类肿瘤-免疫系统动力学性态的全局分析
基于肿瘤细胞对免疫效应细胞的增殖有刺激和抑制两方面作用的事实, 将其
综合作用以可正可负的作用率系数来描述. 完整分析了肿瘤细胞与效应细胞相互作用
的动力学模型的全局性态, 发现了该模型会发生鞍结点分支和双稳定现象, 使得肿瘤
增殖的最终结果依赖于初始状态, 并且得到了相应的阈值条件. 同时, 还具体分析了效
应细胞的固有输入率与肿瘤细胞对效应细胞的作用率系数对模型动力学性态的影响.
所得结果显示当肿瘤细胞对效应细胞的抑制作用足够强时, 模型会有复杂的动力学性态.
关键词：
肿瘤免疫,
平衡点,
稳定性,
鞍结点分支
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