随机瘤免疫相互作用模型与外部治疗和时间延迟:一个最佳控制问题
H J Alsakaji1, F A Rihan1, K Udhayakumar2
1Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, UAE.
Mathematical biosciences and engineering : MBE
|December 5, 2023
概括
这项研究探讨了使用随机模型对瘤免疫动态的最佳控制. 白噪声和时间延迟显著影响瘤生长,在特定条件下,噪声可能会减少瘤细胞.
科学领域:
- 数学瘤学数学瘤学
- 系统生物学 系统生物学
- 随机微分方程 随机微分方程 随机微分方程
背景情况:
- 瘤-免疫相互作用是复杂的,受到随机因素和治疗干预措施的影响.
- 了解这些动态对于开发有效的癌症疗法至关重要.
- 随机延迟差异模型提供了一个框架来捕捉这些复杂性.
研究的目的:
- 为了研究瘤免疫相互作用的随机延迟差异模型的最佳控制问题 (OC-P).
- 确定瘤灭绝和埃尔戈迪克静止分布的标准.
- 确定最佳的控制策略,以减少瘤生长.
主要方法:
- 利用Lyapunov功能理论建立稳定性和瘤灭绝的条件.
- 开发了一个随机的最佳性系统来指导控制变量选择.
- 采用数值模拟来验证理论发现并评估控制的有效性.
主要成果:
- 白噪声和时间延迟的综合作用显著改变了瘤免疫动态.
- 确定了针对瘤生长减少最优的特定控制变量和策略.
- 证明在某些条件下,白噪声可以抑制瘤细胞的增殖.
结论:
- 这项研究提供了洞察力,通过在随机环境中的最佳策略来控制瘤生长.
- 突出了白噪声在调节瘤免疫系统动态中的双重作用.
- 数字模拟证实了已识别的对照对减少瘤负担的有效性.
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