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On the asymptotic distribution of the size of a stochastic epidemic

Published online by Cambridge University Press:  14 July 2016

Thomas Sellke
Thomas Sellke*
Affiliation:
Purdue University
*
∗ Postal address: Department of Statistics, Purdue University, West Lafayette, IN 47907, U.S.A.
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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.

Keywords

LIMITING POISSON DISTRIBUTIONSTOCHASTIC EPIDEMIC
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 390 - 394
Copyright
Copyright © Applied Probability Trust 1983 

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References

[1] Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and its Applications. Griffin, London.Google Scholar
[2] Daniels, H. E. (1967) The distribution of the total size of an epidemic. Proc. 5th Berkeley Symp. Math. Statist. Prob. 4, 281–293.Google Scholar
[3] Kendall, D. G. (1956) Deterministic and stochastic epidemics in closed populations. Proc. 3rd Berkeley Symp. Math. Statist. Prob. 4, 149–165.Google Scholar
[4] Nagaev, A. V. and Startsev, A. N. (1970) The asymptotic analysis of a stochastic model of an epidemic. Theory Prob. Appl. 15, 98–107.Google Scholar