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一个代数公式,深度学习和一种新的SEIR型模型用于COVID-19大流行
A S Fokas1,2,3, N Dikaios2, Y C Yortsos3
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK.
Royal Society open science
|August 4, 2023
概括
流行病的数学模型可以预测代数,而不是指数,长期平衡. 这项研究开发了一个新的SEIR模型,结合行为变化来实现代数动态,与现实世界的社会模式保持一致,并改进COVID-19预测.
科学领域:
- 流行病学 流行病学
- 数学建模的数学建模
- 计算科学 计算科学
背景情况:
- 具有恒定系数的标准易感-暴露-感染-恢复 (SEIR) 模型预测了指数级流行病平衡.
- 流行病学数据,特别是来自欧洲第一个COVID-19浪潮的数据,表明代数长期动态.
- 以前的预测模型只通过使用代数公式而不是指数公式来实现准确性.
研究的目的:
- 构建一个经过修改的SEIR模型,表现出代数异常行为.
- 调查反映行为变化的非线性流行病依赖参数 (例如社会距离) 的影响.
- 解决参数确定反向问题,并用现实世界的数据验证模型.
主要方法:
- 修改SEIR模型以包括与流行病范围相关的非线性参数.
- 数值方法可稳定地解决反向问题以确定模型参数.
- 深度学习的应用,以评估代数预测模型的最佳性.
主要成果:
- 开发的SEIR模型展示了非对称的代数行为,与社会系统中观察到的权力规律动态一致.
- 使用可靠的流行病学数据实现了准确的参数确定.
- 深度学习分析证实了代数预测方法相对于指数方法的最佳性.
结论:
- 流行病的动态,特别是长期趋势,可以更准确地用代数模型来表示,而不是指数模型.
- 纳入非线性,行为依赖的参数对于现实的流行病建模至关重要.
- 该研究为改善流行病预测和了解社会动态提供了强有力的框架.
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