This paper shows how existing methods of time series analysis and modeling can be exploited in novel ways to monitor and forecast the COVID-19 epidemic. In the past, epidemics have been monitored by various statistical and model metrics, such as evaluation of the effective reproduction number, $R\left(t\right)$. However, $R\left(t\right)$ can be difficult and time consuming to compute. This paper suggests two relatively simple data-based metrics that could be used in conjunction with $R\left(t\right)$ estimation and provide rapid indicators of how the epidemic’s dynamic behavior is progressing. The new metrics are the epidemic rate of change (RC) and a related state-dependent response rate parameter (RP), recursive estimates of which are obtained from dynamic harmonic and dynamic linear regression (DHR and DLR) algorithms. Their effectiveness is illustrated by the analysis of COVID-19 data in the UK and Italy. The paper also shows how similar methodology, combined with the refined instrumental variable method for estimating hybrid Box–Jenkins models of linear dynamic systems (RIVC), can be used to relate the daily death numbers in the Italian and UK epidemics and then provide 15-day-ahead forecasts of the UK daily death numbers. The same approach can be used to model and forecast the UK epidemic based on the daily number of COVID-19 patients in UK hospitals. Finally, the paper speculates on how the state-dependent parameter (SDP) modeling procedures may provide data-based insight into a nonlinear differential equation model for epidemics such as COVID-19.

本文展示了如何以新颖的方式利用现有的时间序列分析和建模方法来监测和预测 COVID-19 流行病。过去，流行病是通过各种统计和模型指标来监测的，例如有效繁殖数的评估，$R\left(吨\right)$. 然而，$R\left(吨\right)$计算起来可能很困难且耗时。本文提出了两个相对简单的基于数据的指标，可以与$R\left(吨\right)$估计并提供有关流行病动态行为进展情况的快速指标。新指标是流行变化率 (RC) 和相关的状态相关响应率参数 (RP)，其递归估计是从动态谐波和动态线性回归（DHR 和 DLR）算法中获得的。对英国和意大利 COVID-19 数据的分析说明了它们的有效性。该论文还展示了如何将类似的方法与用于估计线性动态系统 (RIVC) 的混合 Box-Jenkins 模型的改进工具变量方法相结合，用于关联意大利和英国流行病中的每日死亡人数，然后提供 15-英国每日死亡人数的日前预测。可以使用相同的方法根据英国医院每天的 COVID-19 患者人数来建模和预测英国的流行病。最后，本文推测了状态相关参数 (SDP) 建模程序如何为 COVID-19 等流行病的非线性微分方程模型提供基于数据的洞察力。