Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-30T19:02:36.316Z Has data issue: false hasContentIssue false
  • English
  • Français

A threshold theorem for the Reed-Frost chain-binomial epidemic

Published online by Cambridge University Press:  14 July 2016

Frank Ball
Frank Ball*
Affiliation:
University of Sussex
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove a threshold theorem for the Reed–Frost chain-binomial model which is analogous to the threshold theorem of Williams (1971) for the general stochastic epidemic. We show that when the population size is large a ‘true epidemic’ occurs with a non-zero probability if and only if an initial infective individual infects on average more than one susceptible individual.

Keywords

EPIDEMICSTHRESHOLD THEOREMSSIZE OF EPIDEMICRANDOM GRAPHTREES
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 153 - 157
Copyright
Copyright © Applied Probability Trust 1983 

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
Clarke, L. E. (1958) Cayley's formula for counting trees. J. London Math. Soc. 33, 471–474.Google Scholar
Ludwig, D. (1975) Final size distributions for epidemics. Math. Biosci. 23, 33–46.Google Scholar
Riordan, J. (1958) An Introduction to Combinatorial Analysis. Princeton University Press, Princeton, NJ.Google Scholar
Williams, T. (1971) An algebraic proof of the threshold theorem for the general stochastic epidemic (abstract). Adv. Appl. Prob. 3, 223.CrossRefGoogle Scholar