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瘤-免疫动态的数学建模:稳定性,控制和同步通过分数计算和数值优化

Safoura Rezaei Aderyani^1,2, Reza Saadati³, Fatemeh Rezaei Aderyani⁴

¹School of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, Iran.

Scientific reports

|August 8, 2025

概括

这项研究提出了两种对瘤与免疫系统相互作用的随机数学模型. 新的分数-分数和分数差异方程为癌症动态和免疫反应提供了更深入的见解.

科学领域:

数学生物学数学生物学
免疫学免疫学免疫学
计算科学计算科学

背景情况:

瘤-免疫系统的动态是复杂的,并受到固有的随机性的影响.
随机建模为生物系统提供了更现实的框架.
了解这些相互作用对于开发有效的癌症疗法至关重要.

研究的目的:

介绍和分析两个不同的瘤免疫相互作用的随机数学模型.
通过使用先进的数学运算符,研究瘤免疫动态的定性和定量方面.
探索模型属性,包括定位,稳定性,可控性和同步性.

主要方法:

开发两个模型:一个使用分数-分数导数 (Atangana-Baleanu运算符),另一个使用卡普托的分数差异方程.
应用固定点定理来确定解决方案的存在和独特性.
使用非线性分析进行稳定性检查,并探索第二个模型的可控性和同步性.
通过拉格朗的断片间波进行数值模拟,以可视化各种参数下的系统行为.

主要成果:

证明了两种模式的良好位置 (解决方案的存在和独特性).
分析了稳定性,可控性和同步性质,提供了对系统动态的全面了解.
数字模拟揭示了瘤和免疫细胞之间的复杂相互作用,提供了视觉洞察力.
随机框架在描绘瘤与免疫相互作用时增强了现实主义.

结论:

开发的随机模型为研究瘤免疫动态提供了一个强大的数学框架.
分数-分数和分数差异方法为癌症-免疫细胞相互作用提供了新的视角.
数字模拟突出了这些复杂的生物过程的实际含义和动态特征.

关键词:

亚当斯-巴什福斯方法生物同步生物同步癌症的动态癌症的动态离散时间系统.碎形-分数衍生品分数衍生品.分数微积分的微积分计算.优化免疫疗法优化免疫疗法数学瘤学数学瘤学数字模拟数字模拟最佳控制理论是最好的控制理论.稳定性分析是一种稳定性分析.瘤免疫模型的建模

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