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The rumour process

Published online by Cambridge University Press:  14 July 2016

Ross Dunstan
Ross Dunstan*
Affiliation:
The Australian National University
*
∗ Present address: The School of Mathematical and Physical Sciences, Murdoch University, Murdoch, WA 6153, Australia.
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Abstract

The general stochastic epidemic model is used as a model for the spread of rumours. Recursive expressions are found for the mean of the final size of each generation of hearers. Simple expressions are found for the generation size and the asymptotic form of its final size in the deterministic model. An approximating process is presented.

Keywords

GENERAL EPIDEMICMEAN FINAL GENERATION SIZESASYMPTOTIC FINAL SIZESAPPROXIMATING PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 759 - 766
Copyright
Copyright © Applied Probability Trust 1982 

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References

Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases, 2nd edn. Griffin, London.Google Scholar
Bartholomew, D. J. (1973) Stochastic Models for Social Processes, 2nd edn. Wiley, London.Google Scholar
Daley, D. J. (1967) Some Aspects of Markov Chains in Queueing Theory and Epidemiology. , The University of Cambridge.Google Scholar
Daley, D. J. and Kendall, D. G. (1965) Stochastic rumours. J. Inst. Math. Appl. 1, 42–55.CrossRefGoogle Scholar
Dunstan, R. (1980) A note on the moments of the final size of the general stochastic epidemic model. J. Appl. Prob. 17, 532–538.CrossRefGoogle Scholar
Faddy, M. J. (1977) Stochastic compartment models as approximations to more general stochastic systems with the general stochastic epidemic as an example. Adv. Appl. Prob. 9, 448–461.Google Scholar
Kendall, D. G. (1956) Deterministic and stochastic epidemics in closed populations. Proc. 3rd Berkeley Symp. Math. Statist. Prob. 4, 149–165.Google Scholar
Waugh, W. A. O'N. (1958) Conditioned Markov processes. Biometrika 45, 241–249.CrossRefGoogle Scholar