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The supersession of one rumour by another

Published online by Cambridge University Press:  14 July 2016

G. K. Osei
Affiliation:
University of Hull
J. W. Thompson
Affiliation:
University of Hull

Abstract

A model is considered for a situation in which one rumour suppresses another in a closed population. The distribution of the maximum value attained by the proportion spreading the weaker rumour is obtained in the asymptotic case, and this is compared with some actual distributions for finite population size. Closer approximations to the latter distributions are obtained.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1977 

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References

Barbour, A. D. (1972) The principle of the diffusion of arbitrary constants. J. Appl. Prob. 9, 519541.Google Scholar
Barbour, A. D. (1974) On a functional central limit theorem for Markov population processes. Adv. Appl. Prob. 6, 2139.CrossRefGoogle Scholar
Barbour, A. D. (1975) The asymptotic behaviour of birth-and-death processes. Adv. Appl. Prob. 7, 2843.Google Scholar
Bartholomew, D. J. (1967) Stochastic Models for Social Processes. Wiley, London.Google Scholar
Daley, D. J. and Kendall, D. G. (1965) Stochastic rumours. J. Inst. Math. Appl. 1, 4255.Google Scholar
Daniels, H. E. (1974) The maximum size of a closed epidemic. Adv. Appl. Prob. 6, 607621.Google Scholar
Dietz, K. (1967) Epidemics and rumours — a survey. J. R. Statist. Soc. A 130, 505528.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
Kurtz, T. G. (1970) Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Prob. 7, 4958.Google Scholar
Kurtz, T. G. (1971) Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Prob. 8, 344356.Google Scholar
Osei, G. K. (1976) Problems Concerning the Diffusion of More Than One Rumour. .Google Scholar