具有延迟的肿瘤免疫系统的稳定性
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1.莆田学院 工程实训中心;2.昆明理工大学 城市学院

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O175?? ????????

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The stability of tumor-immune system with time delay
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    摘要:

    目的 肿瘤免疫系统反映了肿瘤细胞与免疫细胞之间相互作用的复杂动力学机制。文中应用线性稳定性分析方法研究了延迟确定性肿瘤免疫系统的稳定性。方法 在肿瘤免疫系统中,由于免疫细胞识别肿瘤细胞到做出合适反应需要一定的时间,在此过程中考虑时间延迟,采用小延迟泰勒展开对模型进行化简,求解出平衡点。利用线性稳定性分析方法,研究了这些平衡点的稳定性。结果 系统的这些平衡点中,有一个稳定焦点、一个稳定结点和两个鞍点,并且这些平衡点的类型和稳定性都不受延迟影响。结论 数值模拟验证了理论分析的结论。研究的结果有助于深入理解肿瘤免疫反应的动力学机制,对肿瘤的生长及治疗提供参考。

    Abstract:

    Objective The tumor-immune system reflects the complex dynamics underlying the interaction between tumor cells and immune cells. The stability of the deterministic tumor-immune system with time delay is researched by means of linear stability analysis method in this paper. Methods In view of time delay in the tumor-immune system since it takes some time for immune cells to recognize tumor cells to make appropriate responses, then the model is simplified by means of Taylor expansion of small delay, and the equilibria are solved out. By linear stability analysis method, the stability of these equilidria are studied. Results There are a stable focus, a stable node, and two saddles in system. Moreover, the type and stability of these equilibria are not affected by the delay. Conclusions Numerical simulation demonstrates previous conclusions. The results can help to have a deep understanding of the dynamics mechanisms of tumor immune response and provide a reference for tumor growth and treatment.

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  • 收稿日期:2022-04-26
  • 最后修改日期:2022-06-13
  • 录用日期:2022-06-16
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