Questioning the Seasonality of SARS-COV-2: A Fourier Spectral Analysis
Authors: Cappi Riccardo , Casini Luca , Tosi Davide , Roccetti Marco 
Published: January 2022

AbstractObjectivesCOVID-19 recurrent waves have ignited a debate on the role of seasonality in the contagion resurgence. Two opposite positions emerged. Those convinced of a sinusoidal seasonality recurring over one-year period driven by climate. Those believing that a fluctuation of the outbreaks repeats without limits, in the absence of control measures. We studied the series of daily confirmed SARS-CoV-2 cases in 30 different countries (February 2020 - December 2021), investigating the hypothesis of whether seasonal and geographic variations may guide the pandemic trajectory.MethodsWe chose 30 countries from different geographies and climates. With a discrete Fourier transform, we performed a spectral analysis of the series of the daily SARS-CoV-2 infections, looking for peaks in the frequency spectrum that could correspond to a recurrent cycle of a given length. This analysis allows to question whether COVID-19 outbreaks have an observable seasonal periodicity.ResultsAll the 30 investigated countries see the recurrence of at least one COVID-19 wave, repeating over a period in the range 3 - 9 months, with a peak of magnitude at least half as large as that of the highest peak ever experienced since the beginning of the pandemic until December 2021. We also computed the distance in days between the two higher peaks in each country, and then we averaged those values over the 30 countries, yielding a mean of 190 days (SD 100). This suggests that outbreaks may repeat with cycles of different lengths, without a precisely predictable seasonality of one year.ConclusionOur findings suggest that COVID-19 outbreaks are likely to occur worldwide, with cycles of repetition of variable lengths. Our Fourier analysis with 30 different countries has not found evidence in favor of a seasonality that recurs over one-year period, solely or with a precisely fixed periodicity.DesignNot ApplicableSettingNot ApplicableParticipantsNot ApplicableInterventionsNot ApplicablePrimary and Secondary Outcome MeasuresNot ApplicableArticle SummaryStrengths and Limitations of this StudyThe use of a discrete Fourier transform offers the advantage of a temporal decomposition of the time series of the daily SARS-COV-2 cases, allowing to explore the temporal relationships among recurrent outbreaks.Analyzing for each country the various repetition cycles of the outbreaks, along with their magnitudes, represents an appropriate method to question the assumption of a seasonal “rise and fall” structure of COVID-19 assumed to recur, almost exclusively, based on a one-year long period.We have made inferences about the seasonality of COVID-19 from a purely observational study. The problem has been avoided to quantify, precisely, the role attributable to various climatic factors or control measures, like temperatures or vaccination.To take advantage of a natural experiment, the time series of the number of daily SARS-CoV-2 cases were subjected to a discrete Fourier transform without resorting to any form of correction/normalization. The SARS-CoV-2 outbreak (started in December 2021) has not been included in this study as the progression of this wave is still ongoing.This analysis presents a natural limitation in time as the pandemic has been in progress so far, for only two years. The Fourier uncertainty principle may render the results at low frequencies somewhat uncertain given this extremely short time domain.