Department of Psychological Methods, University of Amsterdam, Amsterdam, The Netherlands.
Department of Population Health Sciences, Utrecht University, Utrecht, The Netherlands.
Proc Biol Sci. 2022 Feb 9;289(1968):20211809. doi: 10.1098/rspb.2021.1809.
Early warning indicators based on critical slowing down have been suggested as a model-independent and low-cost tool to anticipate the (re)emergence of infectious diseases. We studied whether such indicators could reliably have anticipated the second COVID-19 wave in European countries. Contrary to theoretical predictions, we found that characteristic early warning indicators generally rather than prior to the second wave. A model explains this unexpected finding as a result of transient dynamics and the multiple timescales of relaxation during a non-stationary epidemic. Particularly, if an epidemic that seems initially contained after a first wave does not fully settle to its new quasi-equilibrium prior to changing circumstances or conditions that force a second wave, then indicators will show a decreasing rather than an increasing trend as a result of the persistent transient trajectory of the first wave. Our simulations show that this lack of timescale separation was to be expected during the second European epidemic wave of COVID-19. Overall, our results emphasize that the theory of critical slowing down applies only when the external forcing of the system across a critical point is slow relative to the internal system dynamics.
基于关键减速的预警指标被提议作为一种独立于模型且低成本的工具，以预测传染病的（再次）出现。我们研究了这些指标是否能够可靠地预测欧洲国家的第二波 COVID-19 疫情。与理论预测相反，我们发现特征预警指标通常是在第二波疫情之后，而不是之前。一个模型将这一意外发现解释为非平稳疫情期间的瞬态动力学和松弛的多个时间尺度的结果。特别是，如果第一波疫情在最初似乎得到控制后，在改变情况或迫使第二波疫情的条件出现之前，没有完全稳定到新的准平衡状态，那么由于第一波疫情的持续瞬态轨迹，指标将显示出下降趋势，而不是上升趋势。我们的模拟表明，在 COVID-19 的第二次欧洲疫情中，这种时间尺度分离的缺乏是可以预期的。总的来说，我们的研究结果强调了只有当系统在临界点处的外部驱动力相对于内部系统动力学较慢时，关键减速理论才适用。
