一类具有肿瘤指数增长的肿瘤-免疫模型研究  

Study on a Tumor-Immune Model with Exponential Growth of Tumor

作　　者：王晓琴 王静静 李建全 WANG Xiaoqin;WANG Jingjing;LI Jianquan(School of Arts and Sciences,Shaanxi University of Science&Technology,Xi’an 710021,China)

机构地区：[1]陕西科技大学文理学院

出　　处：《信阳师范学院学报（自然科学版）》2020年第1期9-14,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11371369)

摘　　要：研究一类具有肿瘤细胞指数增长的肿瘤-免疫模型,确定模型有瘤平衡点的存在条件及其稳定性.通过构造Dulac函数排除模型周期解的存在性,得到模型的全局动力学性态,并用数值模拟显示初始状态对模型动力学系统的影响,包括无瘤区域、有瘤区域和癌症区域的存在性.同时,分析了肿瘤细胞和免疫细胞作用系数对模型动力学系统的影响.By analyzing a tumor-immune model with exponential growth of tumor cells, the existence and stability of the equilibrium of the model are determined. The global dynamic behavior of the model is obtained by constructing Dulac function to exclude the existence of periodic solution. By means of numerical simulation, the dependence of dynamics of the model on the initial states and the possible phase regions including the non-tumorous region, tumorous region and cancer region are given. Again, the impact of the interaction coefficient between tumor cells and immune cells on the dynamic system of the model is discussed.

关 键 词：癌细胞 免疫细胞 平衡点 稳定性 

分 类 号：O175.1[理学—数学]