Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T04:55:23.470Z Has data issue: false hasContentIssue false
  • English
  • Français

The maximum size of a closed epidemic

Published online by Cambridge University Press:  01 July 2016

H. E. Daniels
H. E. Daniels*
Affiliation:
University of Birmingham
Get access Rights & Permissions [Opens in a new window]

Abstract

An approximation is found to the distribution of the maximum number of infectives present at any time during the course of a closed epidemic. The technique used is applicable to a commonly occurring type of random walk problem where there is a curved absorbing boundary which is far from the mean path except over a narrow range.

Keywords

EPIDEMICSRANDOM WALKSCURVED BOUNDARY
Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 4 , December 1974 , pp. 607 - 621
Copyright
Copyright © Applied Probability Trust 1974 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bartlett, M. S. (1966) Stochastic Processes. 2nd ed. Cambridge University Press.Google Scholar
Barbour, A. D. (1972) The principle of the diffusion of arbitrary constants. J. Appl. Prob. 9, 519–541.CrossRefGoogle Scholar
Borovkov, A. A. (1972) Limit theorems for random walks with boundaries. Proc. Sixth Berkeley Symposium 3, 19–30.Google Scholar
Daniels, H. E. (1945) The statistical theory of the strength of bundles of threads. Proc. Roy. Soc. London A 183, 405–435.Google Scholar
Daniels, H. E. (1963) The Poisson process with a curved absorbing boundary. Bull. Inst. Internat. Statist. 34th Session 40, 994–1008.Google Scholar
Daniels, H. E. (1967) The distribution of the total size of an epidemic. Proc. Fifth Berkeley Symposium 4, 281–293.Google Scholar
Nagaev, A. V. and Startsev, A. N. (1970) The asymptotic analysis of a stochastic model of an epidemic. Theor. Probability Appl. 15, 98–107.CrossRefGoogle Scholar