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 ni 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 (ϕi, Ni) distribution, for total infection count Ni. 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 ϕi 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 (Pτ < 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 ϕi model appears to be an effective detector of suspiciously low statistical noise in the national SARS-CoV-2 daily infection counts.