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 $\phi _i^{\prime}$ infections per cluster, dividing any daily count n i into $n_i/ _i^{\prime}$ ‘clusters’, for ‘country’ i . We assume that ${n_i}/\phi _i^{\prime}$ 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 $P_{ij}^{\prime}$ of the observation. The $P_{ij}^{\prime}$ values should be uniformly distributed. We find the value $\phi_i$ that minimises the Kolmogorov–Smirnov distance from a uniform distribution. We investigate the ( ϕ 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 ϕ 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 $\phi _i^{28} < 0.1$. Tajikistan, Turkey, Russia, Belarus, Albania, United Arab Emirates and Nicaragua have preferred models that are also sub-Poissonian, with $\phi _i^{28} < 0.5$. A statistically significant ( P τ < 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 ϕ i model appears to be an effective detector of suspiciously low statistical noise in the national SARS-CoV-2 daily infection counts.