瘤-免疫系统相互作用模型中的振荡与免疫反应延迟
Zhaoxuan Huo1, Jicai Huang1, Yang Kuang2
1School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, P. R. China.
Mathematical medicine and biology : a journal of the IMA
|September 17, 2024
概括
这项研究模拟了与延迟反应的瘤-免疫系统相互作用. 时间延迟极大地影响瘤平衡的稳定性,并可以诱导复杂的振荡,影响疾病的动态.
科学领域:
- 数学生物学 数学生物学
- 免疫学 免疫学 免疫学
- 动态系统理论 动态系统理论
背景情况:
- 瘤-免疫系统的动态是复杂的,受反应时间的影响.
- 了解这些相互作用对于开发有效的癌症疗法至关重要.
- 以前的模型往往简化了免疫反应或时间延迟.
研究的目的:
- 研究免疫反应延迟对瘤免疫系统动态的影响.
- 在不同的条件下分析瘤平衡的存在和稳定性.
- 探索因时间延迟而产生的分叉和复杂的振荡模式.
主要方法:
- 开发一种包含非单调免疫反应功能和时间延迟的数学模型.
- 分析瘤平衡及其稳定性.
- 应用Hopf分叉理论 (本地和全球) 来识别关键延迟和分叉解决方案.
- 数字模拟用于验证理论发现并观察复杂的动态.
主要成果:
- 模型显示一个,两个或三个瘤平衡,取决于条件.
- 时间延迟会影响低瘤平衡的稳定性,导致在临界延迟时局部Hopf分叉.
- 由于时间延迟,出现周期性解决方案 (包括放松振荡和复杂模式).
- 数字模拟证实了理论预测.
结论:
- 免疫反应延迟是瘤免疫系统动态的一个关键因素.
- 时间延迟可能会破坏平衡,并产生复杂的,可能有害的振荡.
- 这些发现提供了关于时机在免疫监测和癌症进展中的作用的见解.
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