Anti-clustering 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 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. 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 Algeria has a preferred model that is strongly sub-Poissonian, with phi^{28}_i<0.1. Tajikistan, Turkey, Russia, Belarus, Albania, United Arab Emirates and Nicaragua have preferred models that are also sub-Poissonian, with phi^{28}_i<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 (PFI2020), 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.