在一个时空流行病模型中的分叉和混乱动态,具有延迟的最佳控制,随机过程和灵敏度分析
Arjun Kumar1, Uma S Dubey2, Balram Dubey1
1Department of Mathematics, BITS Pilani, Pilani Campus, Pilani 333031, Rajasthan, India.
Chaos (Woodbury, N.Y.)
|March 27, 2025
概括
这项研究开发了一种流行病模型,包括抑制措施和有限的治疗,分析稳定性,混乱和控制策略. 数字模拟验证了COVID-19和HIV/AIDS数据的发现,突出了人口抑制效应.
科学领域:
- 数学生物学 数学生物学
- 流行病学 流行病学
- 动态系统 动态系统
背景情况:
- 流行病建模对于了解疾病传播至关重要.
- 贝丁顿-德安吉利斯发病率和霍林II型治疗率提供了对人口动态和资源限制的见解.
- 抑制性行为和治疗设施的限制显著影响疾病传播.
研究的目的:
- 引入和分析一种具有特定发病率和治疗率的新型流行病模型.
- 调查拟议模型的稳定性,分叉和混乱动态.
- 探索时间延迟,最佳控制策略,随机性和空间模式对疾病传播的影响.
主要方法:
- 对模型定位,局部和全球稳定性以及共维分叉 (1和2) 的分析.
- 时间延迟,混沌理论,灵敏度分析 (PRCC,EFAST) 和最佳控制 (Pontryagin的最大原则) 的整合.
- 使用连续时间马尔科夫链,分支过程近似和噪声诱导的模式形成开发一个随机模型.
主要成果:
- 展示混乱,并识别导致混乱动态和控制的条件.
- 对疾病灭绝概率和流行病发生率的分析估计.
- 识别图灵不稳定性标准和产生噪声诱导的模式.
结论:
- 该研究使用各种建模技术对流行病动态进行了全面分析.
- 模型参数使用COVID-19 (波兰) 和HIV/AIDS (印度) 数据进行估计,结果通过数值模拟验证.
- 特别强调了易受感染和受感染人群对疾病动态的抑制作用的重要性.
相关概念视频
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