混合竞争模型的动力学和分支与适应性癌症治疗的应用
Huansheng Sun1, Biao Tang1, Jonathan E Forde2
1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, PR China.
Mathematical biosciences
|January 29, 2026
概括
适应疗法使用细胞竞争来对抗癌症药物耐药性. 数学建模显示,以值为基础的方法,而不仅仅是最大杀伤率,优化了治疗结果并延长了生存时间.
科学领域:
- 数学瘤学数学瘤学
- 癌症治疗方法 癌症治疗方法
- 计算生物学 计算生物学
背景情况:
- 适应疗法是一种癌症治疗策略,利用药物敏感细胞和耐药细胞之间的竞争来克服耐药性.
- 适应性治疗的数学基础尚未完全理解,这在优化干预时间和强度方面带来了挑战.
研究的目的:
- 开发和分析适应性治疗的数学模型,包括定期瘤监测和基于值的干预措施.
- 在提出的模型中调查周期性解决方案的存在和稳定性.
- 探索关键参数 (如值和监测期) 对治疗结果的影响.
主要方法:
- 开发一种与药物敏感性和耐药性细胞群体的瘤生长竞争模型.
- 应用分叉理论来分析周期性溶液的存在和稳定性.
- 数字模拟用于研究参数依赖性和治疗失败动态.
主要成果:
- 证明新型 (l,m) T 边界周期解及其稳定性的分析.
- 使用分叉理论证明正周期解的存在和稳定性.
- 数字发现表明,治疗失败的时间取决于敏感细胞的杀死率,具有平原效应.
结论:
- 提高敏感细胞的杀死率并不能保证适应性治疗的最佳治疗结果.
- 实施干预措施的门值可以延长患者的生存时间.
- 基于值的适应疗法通过管理细胞群动态来控制瘤的治疗效益.
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