Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-01T08:17:58.981Z Has data issue: false hasContentIssue false
  • English
  • Français

The area under the infectives trajectory of the general stochastic epidemic

Published online by Cambridge University Press:  14 July 2016

F. Downton
F. Downton*
Affiliation:
University of Birmingham
Get access Rights & Permissions [Opens in a new window]

Abstract

If the cost of an epidemic is a linear function of the number of persons infected at any time, the total cost depends upon the area under the infectives trajectory. This note uses a combinatorial argument to show that for the general stochastic epidemic the distribution of this area may be expressed in terms of the probabilities of the ultimate size of the epidemic.

Keywords

GENERAL STOCHASTIC EPIDEMICEPIDEMIC COSTINFECTIVES TRAJECTORYSTOCHASTIC INTEGRALSSIZE OF EPIDEMICS
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 414 - 417
Copyright
Copyright © Applied Probability Trust 1972 

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

Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Griffin, London.Google Scholar
Daniels, H. E. (1967) The distribution of the total size of an epidemic. Proc. Fifth Berkeley Symp. 4, 281–293.Google Scholar
Downton, F. (1967) A note on the ultimate size of a stochastic epidemic. Biometrika 54, 314–316.Google Scholar
Downton, F. (1968) The ultimate size of carrier-borne epidemics. Biometrika 55, 277–289.Google Scholar
Jerwood, D. (1970) A note on the cost of the simple epidemic. J. Appl. Prob. 7, 440–443.Google Scholar
Jerwood, D. (1971) Cost of Epidemics. , University of Sheffield.Google Scholar
Kermack, W. O. and Mckendrick, A. G. (1927) Contributions to the mathematical theory of epidemics. Proc. Roy. Soc. A 115, 700–721.Google Scholar