考虑复合治疗及分布时滞的肿瘤-免疫动力学模型  

A Tumor-Immune Dynamical Model with Compound Therapy and Distributed Delay

作　　者：邵敏 张国洪[1] SHAO Min;ZHANG Guo-hong(School of Mathematics and Statistic, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2021年第3期111-118,共8页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11701472).

摘　　要：假设免疫细胞由肿瘤激发生成并依据logistic自然增长,建立了一个考虑化疗、免疫治疗及免疫激发分布时滞的肿瘤免疫动力学模型.首先在无时滞的情况下,得到控制和清除肿瘤细胞的阈值条件,发现只要化疗药物浓度高,则可以直接清除肿瘤,但此时免疫系统处于较低水平;如果结合化疗和免疫治疗,则可以在保持免疫系统处于较高水平条件下清除肿瘤.接着研究了免疫激发分布时滞对系统动力学性态的影响,得到了在正平衡点处产生Hopf分支的条件,发现当平均时滞处于中间水平时可能导致系统产生周期震荡的现象,进而可以解释肿瘤的长期复发现象.This article assumes that the immune cells are generated by tumor stimulation and are based on Logistic natural growth.A tumor-immune dynamical model that considers chemotherapy,immunotherapy and immune-stimulated distributed delay has been discussed.First,the threshold conditions for controlling and clearing tumor cells were obtained without delay.It was found that as long as the concentration of chemotherapeutic drug was high,the tumor can be cleared,but the immune system was at a low level.If combined with chemotherapy and immunotherapy,the tumor can be cleared while keeping the immune system at a high level.Then,the effect of immune-stimulated distributed delay on the dynamics of the system was studied,and the conditions for Hopf bifurcation at the positive equilibrium point were obtained.It was found that when the average delay was at an intermediate level,the system could cause periodic oscillation phenomena,which could explain the tumor's long-term recurrence.

关 键 词：复合治疗 LOGISTIC增长 分布时滞 稳定性 HOPF分支 

分 类 号：O175[理学—数学]