一种结合神经ODE-贝叶斯优化方法,用于解决免疫记忆修改后的SIR模型的动态和估计参数
Donglin Liu1, Alexandros Sopasakis1
1Department of Mathematics, Lund University, 22362 Lund, Skåne, Sweden.
Heliyon
|October 11, 2024
概括
这项研究引入了一种混合方法,将神经普通微分方程 (NODE) 和贝叶斯优化相结合,用于建模传染病动态. 该方法准确地预测感染峰值,使用具有免疫记忆的修改后的易受感染-移除 (SIR) 模型.
科学领域:
- 流行病学 流行病学
- 计算生物学 计算生物学
- 数学建模的数学建模
背景情况:
- 传统的流行病学模型往往简化了疾病的动态.
- 纳入免疫记忆和时间延迟等因素对于准确的传染病建模至关重要.
- 现有的方法可能会在复杂的整微分方程和参数估计方面扎.
研究的目的:
- 开发一种新的混合方法,将神经普通微分方程 (NODE) 与贝叶斯优化集成在一起.
- 模拟和估计修改时间延迟易受感染移除 (SIR) 模型的参数,其中包括免疫记忆.
- 为了提高短期和长期传染病动态的预测准确度.
主要方法:
- 提出了一种混合方法,将NODE与贝叶斯优化结合起来.
- 修改了具有免疫记忆的时间延迟SIR模型,并以整微分方程的形式制定.
- 使用Runge-Kutta解决器扩展了NODE框架,以处理参数和动态学习的卷积积分.
- 贝叶斯优化被用来提高预测准确性,特别是对于长期动态.
主要成果:
- 混合模型成功地从墨西哥,南非和韩国的COVID-19数据中学习了时间依赖的参数.
- 确切的短期和长期预测感染动态实现了.
- 该模型证明了能够预测具有显著领先时间的感染峰值的能力.
结论:
- 拟议的混合NODE和贝叶斯优化方法为分析和预测传染病爆发提供了强大的工具.
- 这种方法有效地捕捉了流行病学模型中的复杂动态,包括时间延迟和免疫记忆.
- 这些发现为公共卫生响应提供了宝贵的见解,通过早期和准确预测感染峰值.
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