霍普夫分叉
稳定性理论
理论(学习稳定性)
数学
国家(计算机科学)
分叉
免疫系统
应用数学
纯数学
统计物理学
物理
计算机科学
量子力学
非线性系统
生物
算法
免疫学
机器学习
作者
Zhonghu Luo,Zijian Liu,Yuanshun Tan
标识
DOI:10.1142/s0218127423500773
摘要
In this paper, we propose and analyze an age-structured tumor immune model with time delay. We divide immune cells into two kinds. One is those whose growth is independent of tumor and the other is those whose growth depends on the simulation of the tumor. For these cells, their physiological ages are considered. A mature time delay [Formula: see text] is introduced to the tumor-simulation-dependent immune cells to restrict those cells who participate in the immune response to grow to a minimum physiological age. The existence and stability threshold [Formula: see text] is established for the tumor-free equilibrium state. If [Formula: see text], the tumor-free equilibrium state is both locally and globally asymptotically stable. Whereas, when [Formula: see text], the tumor equilibrium state is locally asymptotically stable if [Formula: see text] and a Hopf bifurcation occurs when [Formula: see text] passes through the threshold [Formula: see text]. This may partly explain the periodic recurrence of some tumors. Finally, theoretical results are verified by some numerical simulations.
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