key: cord-0720869-ofbn5c5d
authors: Bukhari, Qasim; Jameel, Yusuf; Massaro, Joseph M.; D’Agostino, Ralph B.; Khan, Sheraz
title: Periodic Oscillations in Daily Reported Infections and Deaths for Coronavirus Disease 2019
date: 2020-08-17
journal: JAMA Netw Open
DOI: 10.1001/jamanetworkopen.2020.17521
sha: 24df8c7f26ca6ed01909c72609a7aaad49c3810b
doc_id: 720869
cord_uid: ofbn5c5d

This cross-sectional study investigates oscillatory patterns in daily reported infections and deaths for coronavirus disease 2019.

The data for the Figure were programmatically retrieved from Worldometer (https://www.worldometers.info/coronavirus/country/) using python package Beautiful Soup (https://pypi.org/project/beautifulsoup4/).

To remove high frequency fluctuations in the daily new cases and deaths, we applied the moving average filter 1 of three days. Moving average is the most common filter in signal processing and operates by averaging a number of points from the input signal ( ) to produce each point in the output signal ( ). Mathematically:

Where is the number of points in the moving average.

The 

The resulting time series were band-pass filtered in the periodicity of oscillation identify by the welch method using mne-python. 4

The analytic signal ̂( ) was calculated by combining the filtered time series with its Hilbert transform 5 into a complex time series as implemented in SciPy 3 :

Where ℋ represents the Hilbert Transform operation

The resulting time series ( ) can be seen as a rotating vector in the complex plane whose length corresponds to the envelope of the original time series ( ) and whose phase grows according to the dominant frequency. The instantaneous phase angle was computed in the complex plane as:

© 2020 Bukhari Q et al. JAMA Network Open.

The rose plot in panel C of the Figure represents the polar histogram of phase angle difference between daily new cases and deaths, mathematically:

The code and data API for reproducing our analysis reported in this article are available at https://github.com/SherazKhan/covid_oscillations.

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