On the asymptotic distribution of the size of a stochastic epidemic

1983/06/01 by Thomas Sellke · 6 citations
Mathematics · Medicine · Biochemistry, Genetics and Molecular Biology · #COVID-19 epidemiological studies #Mathematical and Theoretical Epidemiology and Ecology Models #Evolution and Genetic Dynamics

paper · doi:10.2307/3213811

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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