Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T17:22:06.167Z Has data issue: false hasContentIssue false
  • English
  • Français

A useful random time-scale transformation for the standard epidemic model

Published online by Cambridge University Press:  14 July 2016

Ray Watson
Ray Watson*
Affiliation:
University of Melbourne
*
∗ Postal address: Department of Statistics, Richard Berry Building, University of Melbourne, Parkville, Victoria 3052, Australia.
Get accessRights & Permissions [Opens in a new window]

Abstract

In this paper it is shown that a random time-scale transformation leads to a simple derivation of some asymptotic results describing the progress of a major outbreak in the standard epidemic model. These results find application in approximation of the size distribution and in estimation of the threshold parameter.

Keywords

STANDARD EPIDEMIC MODELRANDOM TIME-SCALE TRANSFORMATIONASYMPTOTIC RESULTSESTIMATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980, pp. 324 - 332
Copyright
Copyright © Applied Probability Trust 1980 

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.)

Article purchase

Temporarily unavailable

References

Bailey, N. T. J. (1953) The total size of a general stochastic epidemic. Biometrika 40, 177–185.Google Scholar
Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases. Griffin, London.Google Scholar
Bailey, N. T. J. and Thomas, A. S. (1971) The estimation of parameters from population data on the general stochastic epidemic. Theoret. Popn. Biol. 2, 253–270.Google Scholar
Barbour, A. D. (1974) On a functional central limit theorem for Markov population processes. Adv. Appl. Prob. 6, 21–39.Google Scholar
Becker, N. G. (1970) Mathematical Models in Epidemiology and Related Fields. Ph.D. Thesis, University of Sheffield.Google Scholar
Downton, F. (1972) The area under the infectives trajectory of the general stochastic epidemic. J. Appl. Prob. 9, 414–417 and 873–876.CrossRefGoogle Scholar
Gani, J. (1973) Point processes in epidemiology. In Stochastic Point Processes, ed. Lewis, P. A. W., Wiley, New York, 756–773.Google Scholar
Gani, J. and Jerwood, D. (1972) The cost of a general stochastic epidemic. J. Appl. Prob. 9, 257–269.CrossRefGoogle Scholar
Jerwood, D. (1971) Cost of Epidemics. Ph.D. Thesis, University of Sheffield.Google Scholar
Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes. Academic Press, New York.Google Scholar
Nagaev, A. V. and Startsev, A. V. (1970) The asymptotic analysis of a stochastic model of an epidemic. Theory Prob. Appl. 15, 98–107.Google Scholar
Watson, R. K. (1977) Stochastic Population Models. Ph. D. Thesis, University of Melbourne.Google Scholar
Watson, R. K. (1980) An application of a martingale central limit theorem to the standard epidemic model. Stoch. Proc. Appl. To appear.Google Scholar