考虑化疗、免疫治疗及分布时滞的肿瘤动力学模型  

On Dynamics of a Tumor-Immune Model Considering Chemotherapy,Immunotherapy and Distributed Delay

作　　者：王苗 张国洪[1] WANG Miao;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1期153-159,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11701472,11871403).

摘　　要：研究了一个描述体内肿瘤细胞与免疫系统相互作用的动力学模型,分析了化疗、免疫治疗及分布时滞对系统动力学性态的影响.发现只要化疗效果足够好,肿瘤细胞就一定会被清除掉;而如果要在免疫细胞持续生存的条件下清除掉肿瘤细胞,需要保证在化疗效果较好的前提下,加大免疫治疗的强度;当免疫治疗强度较大,化疗效果较小时,肿瘤与免疫细胞可能共存.同时还发现,分布时滞的引入可能导致系统产生周期震荡现象,进而可以解释肿瘤的复发现象.In this paper,a kinetic model describing the interaction between tumor cells and the immune system in humans has been proposed with the consideration of the effect of chemotherapy,immunotherapy,and distribution delays on the dynamics of the system.It has been found that,as long as the effect of chemotherapy is good enough,tumor cells will be eliminated;and if the tumors can be destroyed when the immune cells continue to survive,it is needed to increase the intensity of immunotherapy under the premise of good chemotherapy effect;when the intensity of immunotherapy is large and the effect of chemotherapy is small,tumors and immune cells may coexist.At the same time,it has also been found that the introduction of distributed delays may lead to the appearance of periodic oscillation phenomena,which can explain the recurrence of the tumors.

关 键 词：化疗 免疫治疗 分布时滞 稳定性 周期震荡 

分 类 号：O175[理学—基础数学]