肿瘤免疫系统的延迟对稳定性的影响
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福建省中青年教师教育科研项目(JAT200515)


Effects of Delay in Tumor-Immune System on Stability
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    摘要:

    目的 应用线性稳定性分析方法研究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,研究平衡点的稳定性。 再利用数值计算方法模拟系统及平衡点附近的轨线图,用以验证理论分析的结果。 结果 在小延迟条件下,系统共有 4 个有意义的平衡点,分别是1 个稳定焦点、1 个稳定结点和 2 个鞍点,并且这些平衡点的类型和稳定性都不受延迟影响,数值模拟验证了理论分析的结论。 结论 在小延迟条件下,系统平衡点的类型和稳定性不受延迟影响。 研究结果有助于深入理解肿瘤免疫反应的动力学机制,为肿瘤的生长及治疗提供参考

    Abstract:

    Objective To study stability of the deterministic tumor-immune system with time delay by means of linear stability analysis method. Methods In tumor-immune system, since it took some time for immune cells to recognize tumor cells and respond appropriately, time delay was considered in this process, then the model was simplified by using Taylor expansion of small delay, and the equilibrium points were solved out. By linear stability analysis method, the stability of these equilibrium points was studied. Finally, the trajectory of the system and that around each equilibrium point were simulated by numerical calculation method, so as to verify the result of theoretical analysis. Results The system had four meaningful equilibrium points with small delay, including a stable focus, a stable node, and two saddles. Moreover, the type and stability of these equilibrium points were not affected by the delay. Numerical simulation demonstrated the conclusion from theoretical analysis. Conclusions Under the condition of small delay, the type and stability of equilibrium points in the system are not affected by the delay. The results are helpful to further understand dynamic mechanisms of tumor immune response, and provide references for tumor growth and treatment

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李阳娟,段卫龙.肿瘤免疫系统的延迟对稳定性的影响[J].医用生物力学,2023,38(2):248-254

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  • 收稿日期:2022-04-26
  • 最后修改日期:2022-06-07
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  • 在线发布日期: 2023-04-25
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