| 张立成,李胜,曹发坤.具有 Allee 效应的非小细胞肺癌模型的敏感性分析及数值仿真[J].高技术通讯(中文),2024,34(10):1098~1109 |
| 具有 Allee 效应的非小细胞肺癌模型的敏感性分析及数值仿真 |
| Sensitivity analysis and numerical simulation of non-small cell lung cancer model under Allee effect |
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| DOI：10. 3772 / j. issn. 1002-0470. 2024. 10. 009 |
| 中文关键词: 肿瘤-免疫系统; 数学建模; Allee 效应; 敏感性分析 |
| 英文关键词: tumor-immune system, mathematical modeling, Allee effect, sensitivity analysis |
| 基金项目: |
| 作者 | 单位 | | 张立成 | (浙江工业大学信息工程学院 杭州 310023) | | 李胜 | | | 曹发坤 | |
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| 中文摘要: |
| Allee 效应是一种描述了种群密度与物种的平均个体适合度之间相关性的生物学现象。 这种现象解释了一些生物在低密度状态下生长偏离指数生长的原因。 应用数学和生物学理论,结合计算机技术,建立具有 Allee 效应的肿瘤-免疫模型对于了解肿瘤生长过程和优化治疗方案有着重要意义。 考虑肿瘤-免疫环境,提出一个具有 5 个变量的常微分方程系统描述肿瘤微环境内肿瘤细胞和不同免疫细胞之间的交互,包括肿瘤细胞、自然杀伤(NK)细胞、CD8 + T 细胞、循环淋巴细胞以及化疗药物的浓度,并将 Allee 效应的影响纳入模型。 对于构建的数学模型,通过稳定性分析描述特定参数下模型的动力学性质。使用拉丁超立方抽样/ 偏秩相关系数(LHS / PRCC)方法对模型参数进行敏感性分析,分析并讨论影响肿瘤生长的最重要的参数。 通过模拟化疗期间细胞种群的变化,分析 Allee 效应对于化疗方案选择的影响。 |
| 英文摘要: |
| The Allee effect is a biological phenomenon that describes the correlation between population density and the
average individual fitness of a species. This phenomenon explains why some organisms deviate from exponential
growth at low densities. Applying mathematical and biological theories, combined with computer technology, estab-
lishing a tumor-immune model with Allee effect is of great significance for understanding tumor growth process and
optimizing treatment plan. Considering the tumor-immune environment, a system of ordinary differential equations
with 5 variables is proposed to describe the interaction between tumor cells and different immune cells in the tumor
microenvironment, including tumor cells, natural killer (NK) cells, CD8 + T cells, concentrations of circulating
lymphocytes and chemotherapeutic drugs. The influence of the Allee effect is included in the model. For the con-
structed mathematical model, the dynamic properties of the model under specific parameters are described through
stability analysis. Sensitivity analysis of model parameters is performed using the Latin hypercube sampling / partial
rank correlation coefficient (LHS / PRCC) method, and the most important parameters affecting tumor growth are
analyzed and discussed. By simulating the changes of cell populations during chemotherapy, the influence of Allee
effect on the choice of chemotherapy regimen is analyzed. |
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