Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T01:53:24.531Z Has data issue: false hasContentIssue false
  • English
  • Français

The cost of a general stochastic epidemic

Published online by Cambridge University Press:  14 July 2016

J. Gani  and
D. Jerwood
J. Gani
Affiliation:
University of Sheffield
D. Jerwood
Affiliation:
University of Bradford
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is concerned with the cost Cis = aWis + bTis (a, b > 0) of a general stochastic epidemic starting with i infectives and s susceptibles; Tis denotes the duration of the epidemic, and Wis the area under the infective curve. The joint Laplace-Stieltjes transform of (Wis, Tis) is studied, and a recursive equation derived for it. The duration Tis and its mean Nis are considered in some detail, as are also Wis and its mean Mis. Using the results obtained, bounds are found for the mean cost of the epidemic.

Keywords

GENERAL STOCHASTIC EPIDEMICDURATIONSTOCHASTIC PATH INTEGRALCOSTBOUNDS FOR COST
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 2 , June 1972 , pp. 257 - 269
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
Bartholomew, D. J. (1967) Stochastic Models for Social Processes. Wiley, New York.Google Scholar
Bartlett, M. S. (1960) Stochastic Population Models in Ecology and Epidemiology. Methuen, London.Google Scholar
Bartlett, M. S. (1961) EquaTIONS FOR STOCHASTIC PATH INTEGRALS. PROC. CAMB. PHIL. SOC. 57, 568–573.Google Scholar
Dietz, K. (1967) Epidemics and rumours: A survey. J. R. Statist. Soc. A 130, 505–528.Google Scholar
Downton, F. (1972) The area under the infectives trajectory of the general stochastic epidemic. J. Appl. Prob. 9, 414–417.Google Scholar
Gani, J. and Mcneil, D. R. (1971) Joint distributions of random variables and their integrals for certain birth-death and diffusion processes. Adv. Appl. Prob. 3, 339–352.Google Scholar
Jerwood, D. (1970) A note on the cost of the simple epidemic. J. Appl. Prob. 7, 440–443.CrossRefGoogle Scholar
Jerwood, D. (1971) Cost of Epidemics. , Sheffield University.Google Scholar
Mcneil, D. R. (1970) Integral functionals of birth and death processes and related limiting distributions. Ann. Math. Statist. 41, 480–485.Google Scholar
Puri, Prem S. (1966) On the homogeneous birth-and-death process and its integral. Biometrika 53, 61–71.Google Scholar
Puri, Prem S. (1968) Some further results on the birth-and-death process and its integral. Proc. Camb. Phil. Soc. 64, 141–154.CrossRefGoogle Scholar