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慢性髓性白血病模型中的动力学和分支与最佳免疫反应窗口的慢性髓性白血病模型

Artur César Fassoni¹, Claudio Vidal Diaz², Denis de Carvalho Braga³

¹Instituto de Matemática e Computação, Universidade Federal de Itajubá, Itajubá, Brazil. fassoni@unifei.edu.br.

Journal of mathematical biology

|August 23, 2024

概括

慢性髓性白血病 (CML) 患者可能会由于周期性免疫相互作用而经历瘤水平波动. 这项研究数学模型CML,揭示了捕食者-猎物动态可以解释这些观察到的低级振荡.

科学领域:

数学生物学数学生物学
免疫学免疫学免疫学
在瘤学瘤学.

背景情况:

标准的氨酸激酶抑制剂治疗对大多数慢性髓性白血病 (CML) 患者有效.
在治疗后,许多CML患者表现出无法检测的瘤细胞或低水平的,波动的瘤负载.

研究的目的:

调查观察到的CML瘤动力学是否来自由瘤与免疫相互作用驱动的周期性振荡.
分析CML的数学模型,包括具有最佳激活窗口的免疫反应.

主要方法:

分析一个普通微分方程系统,模拟CML-免疫力学.
研究平衡点稳定性的研究.
严格证明跨临界和霍夫分叉.
使用利亚普诺夫系数检查极限周期的出现和稳定性.
用临床相关参数进行数值模拟.

主要成果:

数学模型证明了跨临界和霍夫分叉,证实了周期性振荡.
霍夫分叉分析揭示了极限周期的出现和稳定性.
使用临床参数的模拟支持了理论发现.
该模型表明,捕食者与猎物的相互作用是观察到的CML瘤负载波动的基础.

结论:

这项研究提供了数学证据,证明瘤与免疫相互作用可以在CML中产生周期性振荡.
在CML患者中观察到的低水平瘤负荷波动可以通过这些周期动态来解释.
这些发现提供了超越标准治疗反应的CML动态的见解.

关键词:

霍夫-双分支线的分支线数学建模的数学建模非线性动力学是一种非线性动力学.瘤-免疫相互作用

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