具有反应扩散的随机肿瘤免疫模型接近最优控制研究  

Near-optimal Control of Stochastic Tumor Immune Model with Reaction Diffusion

作　　者：徐鹤丽 薛文宁 高建国 XU Heli;XUE Wenning;GAO Jianguo(College of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China;Yinchuan Xingqing District Experimental Second Primary School,Yinchuan 750021,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]银川市兴庆区实验第二小学,宁夏银川750021

出　　处：《应用数学》2024年第2期439-455,共17页Mathematica Applicata

基　　金：国家自然科学基金项目(61761002);北方民族大学研究生创新项目(YCX22110)。

摘　　要：本文在Kuznetsov模型基础上考虑随机因素及细胞的反应扩散对模型的影响,建立具有反应扩散的随机肿瘤免疫模型,将注射免疫细胞作为控制策略,提出了随机肿瘤免疫的最优控制问题.然后,利用Hamiltion函数和Ekeland极大值原理研究了接近最优控制的存在性,给出系统接近最优控制的充分条件与必要条件.最后,进行数值模拟验证了主要的结论.In this paper,based on the Kuznetsov model,the stochastic factors and the influence of cell reaction diffusion on the model are considered,a stochastic tumor immunity model with reaction diffusion is established,and the optimal control problem of the stochastic tumor immunity model is proposed by considering the injection of immune cells as a control strategy.Then,the existence of near-optimal control is studied by using the Hamiltion function and the Ekeland maxima principle,and the sufficient condition and the necessary condition for the system near-optimal control are given.Finally,numerical simulation verifies the main conclusions.

关 键 词：反应扩散 随机扰动 接近最优控制 肿瘤免疫模型 

分 类 号：O211.6[理学—概率论与数理统计]