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On the size distribution for some epidemic models

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.
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Abstract

We consider the standard epidemic model and several extensions of this model, including Downton's carrier-borne epidemic model. A random time-scale transformation is used to obtain equations for the size distribution and to derive asymptotic approximations for the size distribution for each of the models

Keywords

APPROXIMATIONEPIDEMIC MODELRANDOM TIME-SCALE TRANSFORMATIONSIZE DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 912 - 921
Copyright
Copyright © Applied Probability Trust 

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References

Anderson, D. A. and Watson, R. K. (1980) On the spread of a disease with gamma distributed latent and infectious periods. Biometrika 67, 191–198.CrossRefGoogle Scholar
Bailey, N. T. J. (1953) The total size of a general stochastic epidemic. Biometrika 40, 177–185.CrossRefGoogle Scholar
Bailey, N. T. J. (1964) Some stochastic models for small epidemics in large populations. Appl. Statist. 13, 9–19.CrossRefGoogle Scholar
Bartlett, M. S. (1955) An Introduction to Stochastic Processes. Cambridge University Press.Google Scholar
Becker, N. G. (1977) On a general stochastic epidemic. Theoret. Popn. Biol. 11, 23–36.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Downton, F. (1968) The ultimate size of carrier-borne epidemics. Biometrika 55, 277–289.CrossRefGoogle Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. Wiley, New York.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
Gani, J. (1967) On the general stochastic epidemic. Proc. 5th Berkeley Symp., Math. Statist. Prob. 4, 271–279.Google Scholar
Watson, R. K. (1980) A useful random time-scale transformation for the standard epidemic model. J. Appl. Prob. 17, 324–332.CrossRefGoogle Scholar
Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–490.CrossRefGoogle ScholarPubMed
Whittle, P. (1955) The outcome of a stochastic epidemic — a note on Bailey's paper. Biometrika 42, 116–122.Google Scholar
Williams, T. (1971) An algebraic proof of the threshold theorem for the general stochastic epidemic. Adv. Appl. Prob. 3, 223.CrossRefGoogle Scholar