Epidemiological waves - types, drivers and modulators in the COVID-19 pandemic

Abstract

Introduction: A discussion of 'waves' of the COVID-19 epidemic in different countries is a part of the national conversation for many, but there is no hard and fast means of delineating these waves in the available data and their connection to waves in the sense of mathematical epidemiology is only tenuous. Methods: We present an algorithm which processes a general time series to identify substantial, significant and sustained periods of increase in the value of the time series, which could reasonably be described as 'observed waves'. This provides an objective means of describing observed waves in time series. Results: The output of the algorithm as applied to epidemiological time series related to COVID-19 corresponds to visual intuition and expert opinion. Inspecting the results of individual countries shows how consecutive observed waves can differ greatly with respect to the case fatality ratio. Furthermore, in large countries, a more detailed analysis shows that consecutive observed waves have different geographical ranges. We also show how waves can be modulated by government interventions and find that early implementation of non-pharmaceutical interventions correlates with a reduced number of observed waves and reduced mortality burden in those waves. Conclusion: It is possible to identify observed waves of disease by algorithmic methods and the results can be fruitfully used to analyse the progression of the epidemic.

EpidemicKabu a new method to identify epidemic waves and their peaks and valleys

“…Our methodology has two parameters to be set but the user and a third one that is optional. Similarly, previous methods have one or more than one parameters to be set by the user [11,13]. We noticed that although epidemicKabu does not set the minimum duration of a wave as in the methodology designed by Harvety et al (2022) [11], the duration in days of our detected waves are in the range stablished by this method.…”

“…Sometimes, as in the case of the United Kingdom curve, the waves detected by this methodology appear not to be in accordance with the statement: a wave requires substantial, significant and sustained periods of increase [11], and it ends when the virus is brought under control and the cases fall substantially or they remain stable over time [13]. However, this could be improved by increasing the kernel value for smoothing the epidemic curve.…”

“…In spite of the different approaches to identify waves, all the previous studies agreed that a complete wave includes a rise in the number of cases, a defined peak, and a decline [4]. Additionally, despite definitional problems, using these descriptive terms has important values for planning and public health [11].…”

“…Additionally, despite definitional problems, using these descriptive terms has important values for planning and public health [11].…”

ModInterv: An automated online software for modeling epidemics

“…In the current version of ModInterv we have implemented a filter based on the relative amplitudes of nearby maxima/minima to reject those that are likely due to fluctuations [19]. We are currently investigating the possibility of using a more selective algorithm recently introduced in the literature for detecting relevant maxima and minima [27]. Another difficulty stems from the often large number of parameters that need to be determined from the chosen empirical data (there are 7𝑁 − 2 free parameters for an epidemic curve with 𝑁 waves).…”