Song Ge, Tian Tianhai, Zhang Xinan
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China.
School of Mathematics, Monash University, Melbourne, VIC 3800, Australia.
Math Biosci Eng. 2020 Dec 4;18(1):373-385. doi: 10.3934/mbe.2021020.
Mathematical models of tumor-immune interactions provide an analytic framework for studying tumor-immune dynamics. In this paper, we present a mathematical model to describe tumor-immune cell interactions, focusing on the role of the natural killer (NK) cells and CD8+ cytotoxic T lymphocytes (CTLs) in immune surveillance. According to the experimental and clinical results, we determine part of the model parameters to reduce the model parameter space. Then we analyze the local geometric properties of the equilibria of model and carry out numerical simulations to verify the conditions for the stability properties of equilibrium points. Numerical results suggest that the host immune system alone is not fully effective against progression of tumor cells, and CTLs play a crucial role in immune surveillance.
肿瘤-免疫相互作用的数学模型为研究肿瘤-免疫动力学提供了一个分析框架。在本文中，我们提出了一个数学模型来描述肿瘤-免疫细胞的相互作用，重点关注自然杀伤（NK）细胞和CD8 + 细胞毒性T淋巴细胞（CTL）在免疫监视中的作用。根据实验和临床结果，我们确定了部分模型参数以缩小模型参数空间。然后我们分析了模型平衡点的局部几何性质，并进行了数值模拟以验证平衡点稳定性性质的条件。数值结果表明，仅宿主免疫系统对肿瘤细胞的进展并不完全有效，而CTL在免疫监视中起着关键作用。
