Overlapping Time Scales Obscure Early Warning Signals of the Second COVID-19 Wave (preprint)

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 time scales 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 time scale 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.

The lighting of the BECONs: A behavioral data science approach to tracking interventions in COVID-19 research (preprint)

The imposition of lockdowns in response to the COVID-19 outbreak has underscored the importance of human behavior in mitigating virus transmission. Scientific study ofinterventions designed to change behavior (e.g., to promote social distancing) requiresmeasures of effectiveness that are fast, that can be assessed through experiments, and that can be investigated without actual virus transmission. This paper presents a methodological approach designed to deliver such indicators. We show that behavioral data, obtainable through tracing apps currently in development, can be used to assess a central concept in epidemiology known as the contact network: a network representation that encodes which individuals have been in physical proximity long enough to transmit the virus. Because behavioral interventions alter the contact network, a comparison of contact networks before and after the intervention can provide information on the effectiveness of the intervention. We coin indicators based on this idea Behavioral Contact Network (BECON) indicators. We examine the performance of three indicators: the Density BECON (based on differences in network density), the Spectral BECON (based on differences in the eigenvector of the adjacency matrix), and the ASPL BECON (based on differences in average shortest path lengths). Using simulations, we show that all three indicators can effectively track the effect of behavioral interventions. Even in conditions with significant amounts of noise, BECON indicators can reliably identify and order effect sizes of interventions. The present paper invites further study of the method as well as practical implementations to test the validity of BECON indicators in real data.