基于微积分计算的结肠癌模型与治疗干预的动态稳定性分析
Ruilei Tai1, Zhaoyang Chen2, Yanling Zhao3
1Laboratory Animal Center, Shanxi Key Laboratory of Experimental Animal Science and Animal Model of Human Disease, Shanxi Medical University, Taiyuan, 030001, China. tairuileimail@163.com.
Scientific reports
|December 10, 2025
概括
这项研究引入了分数顺序结肠癌模型,以优化化疗. 数学分析和模拟揭示了益生菌和T细胞如何影响瘤动态,指导组合治疗策略.
科学领域:
- 数学瘤学数学瘤学
- 免疫疗法建模模型
- 分数计算的应用 分数计算的应用
背景情况:
- 结肠癌对全球健康构成重大挑战.
- 目前用于结肠癌的化学免疫疗法在有效性和毒性方面存在局限性.
- 需要先进的数学模型来优化治疗策略.
研究的目的:
- 开发和分析结肠癌的新型分数顺序数学模型.
- 为了研究益生菌-T细胞-瘤细胞轴内的复杂相互作用.
- 为增强基于益生菌的组合疗法提供理论框架.
主要方法:
- 为结肠癌动态建立一个分数次序微分方程模型.
- 应用固定点理论来证明解决方案的存在和独特性.
- 使用Routh-Hurwitz标准对平衡点的稳定性分析.
- 进行数值模拟以探索分数参数和药物剂量的影响.
主要成果:
- 该模型的解决方案被严格证明存在并是独一无二的.
- 我们得出了分析条件来确定系统平衡的稳定性.
- 数字模拟证明了分数参数 (α) 对系统动态和记忆效应的影响.
- 确定了有效瘤清除的关键药物剂量值.
结论:
- 分数顺序模型为了解结肠癌进展提供了坚实的数学基础.
- 这项研究强调了数学建模在优化化疗疗疗方案方面的潜力.
- 研究结果支持开发更有效,个性化的益生菌基结合治疗结肠癌.
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