在SIRS模型中的振荡
Davide Marenduzzo1, Aidan T Brown1, Craig W Miller1
1School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, UK.
Journal of theoretical biology
|June 14, 2025
概括
该SIRS流行病模型揭示了内在的,非季节性振荡. 这种由免疫力下降所驱动的繁荣衰退周期,解释了像COVID-19这样的反复流行病没有外部因素.
科学领域:
- 流行病学 流行病学
- 数学生物学 数学生物学
- 计算科学 计算科学
背景情况:
- 该SIRS (易感-感染-恢复-易感) 模型描述了疾病的动态.
- 传统模型确定稳定的状态:无病 (I=0) 和特有 (I>0).
- 诸如季节性等外部因素经常被用来解释流行病的波动.
研究的目的:
- 调查SIRS模型的内在动态.
- 探索流行病模型中振荡行为的出现.
- 为了确定免疫力下降是否可以单独驱动定期的流行病周期.
主要方法:
- 对SIRS模型的分析调查.
- 在带有噪声的正方形格子上进行数值模拟.
- 分析模型解决方案以确定稳定状态和振荡.
主要成果:
- 在SIRS模型中,表现出两个稳定的状态:无病和特有.
- 使用噪声或在格子上的实现揭示了第三个状态:正则振荡.
- 这些振荡代表了由免疫力下降所驱动的内在繁荣衰退的流行病周期.
结论:
- 振荡性流行病行为是SIRS模型的内在属性.
- 在大约10周的时间尺度上,免疫力下降可以解释非季节性波动.
- 这种内在的振荡行为可以解释COVID-19 (例如Omicron变种) 等疾病中观察到的模式.
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