简化的SEIRS流行病模型的动力学:全球对称稳定性和神经Lyapunov功能
Yukun Zou1,2, Xiaoxiao Peng1,3, Wei Yang4,5,6
1Research Institute of Intelligent Complex Systems, Fudan University, 220 Handan Road, Shanghai, 200433, China.
Journal of mathematical biology
|June 16, 2024
概括
这项研究引入了传染病传播的新网络模型,揭示了复杂的多体相互作用增加了感染率. 它还验证了模型的有效性.
科学领域:
- 流行病学和网络科学 流行病学和网络科学
- 传染病的数学建模传染病的数学建模
- 复杂系统和机器学习应用程序
背景情况:
- 传染病的传播发生在现实世界的复杂网络上.
- 了解高阶网络结构上的疾病动态至关重要,但具有挑战性.
- 现有的模型往往简化了网络交互,可能缺少关键的传输因素.
研究的目的:
- 在高阶网络上研究具有潜伏期的传染病传播机制.
- 开发和分析一种新的简化的SEIRS (易感-暴露-传染-恢复-易感) 模型.
- 探索机器学习技术的应用,以验证复杂的流行病学模型.
主要方法:
- 开发一个包含简化交互 (多体连接) 的简化SEIRS模型.
- 分析模型的动态,包括存在和局部非对称稳定性.
- 运用神经里亚普诺夫函数来证明全局非对称稳定性,得到数值模拟和分析论证的支持.
主要成果:
- 由于简体网络中的多体连接,在平衡状态下感染个体的比例增加.
- 与现有的低级网络模型相比,已建立的简单的SEIRS模型表现出不同的动态.
- 该模型的全局非对称稳定性通过使用神经莱普诺夫函数成功证明.
结论:
- 多体相互作用显著影响传染病在高阶网络上传播.
- 开发的简化的SEIRS模型为疾病传播动态提供了宝贵的见解.
- 使用神经利亚普诺夫函数为分析网络系统中传染病的复杂动态提供了一种强大的方法.
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