About: 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: $/phi_i /sim/sqrt{N_i}$. 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 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.   Goto Sponge  NotDistinct  Permalink

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  • 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: $/phi_i /sim/sqrt{N_i}$. 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 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.
subject
  • Epidemiology
  • Infectious diseases
  • Hypotension
  • Poisson distribution
  • Conjugate prior distributions
  • Infinitely divisible probability distributions
  • Factorial and binomial topics
  • Location-scale family probability distributions
  • Poisson point processes
  • Types of probability distributions
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