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Asymptotic final-size distribution for some chain-binomial processes

Published online by Cambridge University Press:  01 July 2016

Gianpaolo Scalia-Tomba
Gianpaolo Scalia-Tomba*
Affiliation:
University of Stockholm
*
∗Postal address: Department of Mathematical Statistics, University of Stockholm, Box 6701. S-113 85, Stockholm, Sweden.
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Abstract

The classical Reed-Frost process is generalized by allowing infection probabilities to depend on current epidemic size. Such a process can be imbedded in a simple Markov process derived from i.i.d. waiting times. The final size of the epidemic has the same distribution as the time for the first crossing of a certain linear barrier of the imbedding process. The asymptotic distribution of the final size can be derived from some weak convergence results for the imbedding process. The existence of a distribution determining set of harmonic functions for these chain-binomial processes is also established.

Keywords

EPIDEMIC PROCESSESEMBEDDING
Type
Research Article
Information
Advances in Applied Probability , Volume 17 , Issue 3 , September 1985 , pp. 477 - 495
Copyright
Copyright © Applied Probability Trust 1985 

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References

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