利用非平滑模型分析值策略对癌症治疗的影响
Xingxiao Wu1, Wenjie Qin1, Sanyi Tang2
1Department of Mathematics, Yunnan Minzu University, Kunming, 650500, Yunnan, China.
Mathematical biosciences
|October 11, 2025
概括
这项研究引入了手术免疫治疗的新型动态值模型,优化了治疗时间和强度. 双值策略显著改善瘤控制,同时保持安全的效应细胞水平.
科学领域:
- 数学瘤学数学瘤学
- 免疫学 免疫学 免疫学
- 计算生物学 计算生物学
背景情况:
- 手术免疫疗法是一种有前途的癌症治疗方法,但最佳时间和强度具有挑战性.
- 现有的模型往往缺乏针对治疗优化的动态策略.
- 瘤-免疫系统动态需要复杂的建模,以进行有效的治疗干预.
研究的目的:
- 开发和分析非光滑瘤免疫模型,用于手术免疫治疗的动态值策略.
- 研究单一和双重动态值对治疗结果的影响.
- 使用真实肺癌数据预测患者特异性治疗效果.
主要方法:
- 为单一免疫疗法开发一个依赖状态的冲动微分方程模型.
- 分析Poincaré地图以研究周期性解和混乱 (最大的Lyapunov指数).
- 建立和分析具有双动态值的菲利普洛夫瘤免疫模型,包括滑动模式和伪平衡.
- 使用最小平方法对真实肺癌患者数据进行参数估计.
主要成果:
- 单值模型展示了k顺序的周期性解决方案和混乱的行为,并分析了治疗间隔和频率.
- 双值模型表现出滑动模式,伪平衡和稳定的k顺序周期解,数值模拟证实了混乱现象.
- 使用真实患者数据进行参数估计,可以根据不同的策略预测治疗效果.
结论:
- 双值动态策略优于单值策略,用于控制手术免疫治疗中的瘤细胞密度.
- 双值方法有效地保持有效免疫细胞在安全水平,这对患者安全至关重要.
- 具有动态值的数学建模为优化癌症免疫疗法方案提供了强大的框架.
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