Mathematics Institute, University of Warwick, Coventry, UK.
Mathematics Institute, University of Warwick, Coventry, UK; EPSRC & MRC Centre for Doctoral Training in Mathematics for Real-World Systems, University of Warwick, Coventry, UK.
J Theor Biol. 2022 Dec 7;554:111269. doi: 10.1016/j.jtbi.2022.111269. Epub 2022 Sep 6.
The theory of critical slowing down states that a system displays increasing relaxation times as it approaches a critical transition. These changes can be seen in statistics generated from timeseries data, which can be used as early warning signals of a transition. Such early warning signals would be of value for emerging infectious diseases or to understand when an endemic disease is close to elimination. However, in applications to a variety of epidemiological models there is frequent disagreement with the general theory of critical slowing down, with some indicators performing well on prevalence data but not when applied to incidence data. Furthermore, the alternative theory of critical speeding up predicts contradictory behaviour of early warning signals prior to some stochastic transitions. To investigate the possibility of observing critical speeding up in epidemiological models we characterise the behaviour of common early warning signals in terms of a system's potential surface and noise around a quasi-steady state. We then describe a method to obtain these key features from timeseries data, taking as a case study a version of the SIS model, adapted to demonstrate either critical slowing down or critical speeding up. We show this method accurately reproduces the analytic potential surface and diffusion function, and that these results can be used to determine the behaviour of early warning signals and correctly identify signs of both critical slowing down and critical speeding up.
临界减速状态理论认为，随着系统接近临界点，其弛豫时间会增加。这些变化可以从时间序列数据中生成的统计数据中看出，这些数据可以作为过渡的预警信号。这种早期预警信号对于新发传染病或了解地方病何时接近消除将非常有价值。然而，在应用于各种流行病学模型时，经常与临界减速的一般理论存在分歧，一些指标在流行率数据上表现良好，但在应用于发病率数据时则不然。此外，临界加速的替代理论预测了一些随机跃迁前预警信号的矛盾行为。为了研究在流行病学模型中观察到临界加速的可能性，我们根据系统的势面和准稳态周围的噪声来描述常见预警信号的行为。然后，我们描述了一种从时间序列数据中获取这些关键特征的方法，以 SIS 模型的一个版本为例，该模型经过改编可以展示临界减速或临界加速。我们表明，该方法可以准确地再现分析势面和扩散函数，并且可以使用这些结果来确定预警信号的行为，并正确识别临界减速和临界加速的迹象。
