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Updated: Jan 18, 2026

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模型和分析糖尿病期间的葡萄糖-胰岛素相互作用,在葡萄糖的存在下通过分数动态分析
Parvaiz Ahmad Naik1, Bijal M Yeolekar2, Kolade M Owolabi3
1School of Mathematical Sciences, Chengdu University of Technology, Chengdu 610059, Sichuan, China.
Journal of advanced research
|January 16, 2026
概括
这项研究引入了一个分数顺序的数学模型来分析糖尿病中的葡萄糖-胰岛素-葡萄糖相互作用. 该模型揭示了这些动态如何影响疾病进展,为改善糖尿病管理和治疗策略提供了见解.
科学领域:
- 数学生物学 数学生物学
- 代谢障碍 代谢障碍 代谢障碍
- 控制理论 控制理论
背景情况:
- 糖尿病是一种慢性代谢障碍,其特征是高血糖.
- 葡萄糖,胰岛素和葡萄糖的失调是糖尿病病理生理学的核心.
- 了解这些复杂的相互作用对于开发有效的治疗方法至关重要.
研究的目的:
- 开发和分析葡萄糖-胰岛素-葡萄糖动态的分数级数学模型.
- 为了研究微积分计算对糖尿病进展的影响.
- 评估模型的稳定性和适合可靠预测的位置.
主要方法:
- 使用Anatanga-Baleanu衍生物的分数顺序糖尿病模型的开发.
- 固定点和乌拉姆-海尔斯稳定性的分析.
- 对数值模拟的明确分数欧勒方法的应用.
- 检查定性动态和解决方案的存在/独特性.
主要成果:
- 分数顺序模型捕捉了影响糖尿病进展的记忆效应.
- 参数变化会影响葡萄糖-胰岛素-葡萄糖激素相互作用的峰值幅度和短暂持续时间.
- 该模型在表示疾病动态方面比经典模型更具灵活性.
结论:
- 分数顺序模型为了解糖尿病中的葡萄糖调节提供了一个强大的框架.
- 稳定性和正确位置的分析确保了模型的可靠性.
- 研究结果提供了潜在的治疗点,并指导开发新的糖尿病治疗方法.
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