On the asymptotic distribution of the size of a stochastic epidemic

1983/06/01 by Thomas Sellke · 175 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Applied mathematics #COVID-19 epidemiological studies #Calculus (dental) #Demography #Distribution (mathematics) #Epidemic model #Evolution and Genetic Dynamics #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical economics #Mathematics #Poisson distribution #Poisson process #Population #Simple (philosophy) #Statistical physics #Statistics #Stochastic process

paper · doi:10.2307/3213811

published in Journal of Applied Probability 20(2), 390-394 (Cambridge University Press)

openalex publication_date 1983/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21

Abstract

For a stochastic epidemic of the type considered by Bailey [1] and Kendall [3], Daniels [2] showed that ‘when the threshold is large but the population size is much larger, the distribution of the number remaining uninfected in a large epidemic has approximately the Poisson form.' A simple, intuitive proof is given for this result without use of Daniels's assumption that the original number of infectives is ‘small'. The proof is based on a construction of the epidemic process which is more explicit than the usual description.

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