Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T17:21:56.242Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the total size distribution of epidemic models

Published online by Cambridge University Press:  14 July 2016

Frank Ball
Frank Ball*
Affiliation:
University of Nottingham
*
∗Postal address: Department of Mathematics, The University of Nottingham, University Park Nottingham NG7 2RD, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

A simple coupling argument is used to obtain a new proof of a result of Daniels (1967) concerning the total size distribution of the general stochastic epidemic. The proof admits a straightforward generalisation to multipopulation epidemics and indicates that similar results are unlikely to be available for epidemics with non-exponential infectious periods.

Keywords

SIZE OF EPIDEMICCOUPLINGMULTIPOPULATION EPIDEMIC
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 832 - 836
Copyright
Copyright © Applied Probability Trust 1986 

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

Von Bahr, B. and Martin-Löf, A. (1980) Threshold limit theorems for some epidemic processes. Adv. Appl. Prob. 12, 319–349.Google Scholar
Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. Griffin, London.Google Scholar
Ball, F. G. (1983) The threshold behaviour of epidemic models. J. Appl. Prob. 20, 227–241.Google Scholar
Ball, F. G. (1985) Deterministic and stochastic epidemics with several kinds of susceptibles. Adv. Appl. Prob. 17, 1–22.CrossRefGoogle Scholar
Ball, F. G. (1986) A unified approach to the distribution of total size and total area under the trajectory of infectives for epidemic models. Adv. Appl. Prob. 18, 289–310.Google Scholar
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
Downton, F. (1967) A note on the ultimate size of a general stochastic epidemic. Biometrika 54, 314–316.Google Scholar
Foster, F. G. (1955) A note on Bailey's and Whittle's treatment of a general stochastic epidemic. Biometrika 42, 123–125.Google Scholar
Kendall, W. S. and Saunders, I. W. (1983) Epidemics in competition II: The general epidemic. J. R. Statist. Soc. B 45, 238–244.Google Scholar
Metz, J. A. J. (1978) The epidemic in a closed population with all susceptibles equally vulnerable; some results for large susceptible populations and small initial infections. Acta Biotheoretica 27, 75–123.Google Scholar
Whittle, P. (1955) The outcome of a stochastic epidemic — a note on Bailey's paper. Biometrika 42, 116–122.Google Scholar