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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 decreased rather than increased 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.
A semi-parametric, state-space compartmental model with time-dependent parameters for forecasting COVID-19 cases, hospitalizations and deathsShort-term forecasts of the dynamics of coronavirus disease 2019 (COVID-19) in the period up to its decline following mass vaccination was a task that received much attention but proved difficult to do with high accuracy. However, the availability of standardized forecasts and versioned datasets from this period allows for continued work in this area. Here, we introduce the Gaussian infection state space with time dependence (GISST) forecasting model. We evaluate its performance in one to four weeks ahead forecasts of COVID-19 cases, hospital admissions and deaths in the state of California made with official reports of COVID-19, Google’s mobility reports and vaccination data available each week. Evaluation of these forecasts with a weighted interval score shows them to consistently outperform a naive baseline forecast and often score closer to or better than a high-performing ensemble forecaster. The GISST model also provides parameter estimates for a compartmental model of COVID-19 dynamics, includes a regression submodel for the transmission rate and allows for parameters to vary over time according to a random walk. GISST provides a novel, balanced combination of computational efficiency, model interpretability and applicability to large multivariate datasets that may prove useful in improving the accuracy of infectious disease forecasts.