考虑肿瘤静止细胞的肿瘤-免疫模型的稳定性及最优控制  

Stability and optimal control of a tumor-immunity model considering tumor quiescent cells

作　　者：王茜 刘子建 WANG Xi;LIU Zijian(School of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 402247,China)

机构地区：[1]重庆交通大学数学与统计学院,重庆402247

出　　处：《内江师范学院学报》2025年第2期25-35,共11页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(12271068);重庆市自然科学基金创新发展联合基金项目(CSTB2022NSCQ-LZX0026)。

摘　　要：建立肿瘤增殖细胞、肿瘤静止细胞、细胞毒性T淋巴细胞和自然杀伤细胞的肿瘤-免疫系统相互作用的微分方程模型,证明了解的非负有界性及平衡点的存在性,分析了无肿瘤平衡点的局部和全局稳定性,讨论了正平衡点的局部稳定性.进一步,建立了过继性细胞免疫治疗(ACI)的最优控制模型,研究了最优组合的存在性.最后,通过数值模拟验证了理论推导的结果.A differential equation model is developed for the interaction of tumor immune system with tumor proliferating cells,tumor quiescent cells,cytotoxic T lymphocytes,and natural killer cells.The proof of non-negative boundedness of the solution and the existence of a positive equilibrium point is provided.The analysis includes the examination of local and global stability of the tumor-free equilibrium point and the discussion of the local stability of the positive equilibrium point.Additionally,an optimal control model for Adoptive Cellular Immunotherapy(ACI)is formulated,and the investigation into the existence of optimal combinations is conducted.Finally,numerical simulation is employed to verify the results of the theoretical derivation.

关 键 词：肿瘤细胞 免疫细胞 稳定性 最优控制 

分 类 号：O175.12[理学—数学]