The noise in daily infection counts of an epidemic should be super-Poissonian due to intrinsic epidemiological and administrative clustering. Here, we use this clustering to classify the official national SARS-CoV-2 daily infection counts and check for infection counts that are unusual by being anti-clustered. We adopt a one-parameter model of \phi _i' infections per cluster, dividing any daily count n_i into n_i/\phi _i' ' clusters', for 'country' i. We assume that n_i/\phi _i' on a given day j is drawn from a Poisson distribution whose mean is robustly estimated from the four neighbouring days, and calculate the inferred Poisson probability P _{ij of the observation. The P _{ij values should be uniformly distributed. We find the value \phi_i that minimises the Kolmogorov--Smirnov distance from a uniform distribution. We investigate the (\phi_i, N_i) distribution, for total infection count N_i. We consider consecutive count sequences above a threshold of 50 daily infections. We find that most of the daily infection count sequences are inconsistent with a Poissonian model. All are consistent with the \phi_i model . Clustering increases with total infection count for the full sequences: \phi_i \sim\sqrt{N_i 28-, 14- and 7-day least noisy sequences for several countries are best modelled as sub-Poissonian, suggesting a distinct epidemiological family. The 28-day sequences of DZ , BY, TR, AE have strongly sub-Poissonian preferred models , with \phi_i^{28} < 0.5; and FI, SA , RU, AL, IR have \phi_i^{28} < 3.0. Independent verification may be warranted for those countries with unusually low clustering < 0.05) correlation was found between the lack of media freedom in a country, as represented by a high Reporters sans frontieres Press Freedom Index (PFI^{2020}), and the lack of statistical noise in the country's daily counts. The \phi_i model appears to be an effective detector of suspiciously low statistical noise in the national SARS-CoV-2 daily infection counts} .
The noise in daily infection counts of an epidemic should be super-Poissonian due to intrinsic epidemiological and administrative clustering. Here, we use this clustering to classify the official national SARS-CoV-2 daily infection counts and check for infection counts that are unusually anti-clustered. We adopt a one-parameter model of \phi '_i infections per cluster, dividing any daily count n_i into n_i/\phi '_i ' clusters', for 'country' i. We assume that n_i/\phi '_i on a given day j is drawn from a Poisson distribution whose mean is robustly estimated from the four neighbouring days, and calculate the inferred Poisson probability P '_{ij of the observation. The P '_{ij values should be uniformly distributed. We find the value \phi_i that minimises the Kolmogorov-Smirnov distance from a uniform distribution. We investigate the (\phi_i, N_i) distribution, for total infection count N_i. We find that most of the daily infection count sequences are inconsistent with a Poissonian model. Most are found to be consistent with the \phi_i model , the 28-, 14- and 7-day least noisy sequences for several countries are best modelled as sub-Poissonian, suggesting a distinct epidemiological family. The 28-day least noisy sequence of DZ (Algeria) has a preferred model that is strongly sub-Poissonian , with \phi_i^{28} < 0.1. TJ, TR , RU, BY, AL, AE, and NI have preferred models that are also sub-Poissonian, with \phi_i^{28} < 0.5. A statistically significant (P^{\tau < 0.05) correlation was found between the lack of media freedom in a country, as represented by a high Reporters sans frontieres Press Freedom Index (PFI^{2020}), and the lack of statistical noise in the country's daily counts. The \phi_i model appears to be an effective detector of suspiciously low statistical noise in the national SARS-CoV-2 daily infection counts} .
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