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The distribution of time to extinction in subcritical branching processes: applications to outbreaks of infectious disease

Part of: Inference from stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

C. P. Farrington  and
A. D. Grant
C. P. Farrington*
Affiliation:
Open University
A. D. Grant*
Affiliation:
Public Health Laboratory Service Statistics Unit, London
*
∗Postal address: Statistics department, Faculty of Mathematics and Computing, The Open University, Walton Hall, Milton Keynes, MK7 6AA. Email address: [email protected]
∗∗Postal address: Statistics Unit, PHLS, 61 Colindale Avenue, London, NW9 5EQ.
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Abstract

We consider the distribution of the number of generations to extinction in subcritical branching processes, with particular emphasis on applications to the spread of infectious diseases. We derive the generation distributions for processes with Bernoulli, geometric and Poisson offspring, and discuss some of their distributional and inferential properties. We present applications to the spread of infection in highly vaccinated populations, outbreaks of enteric fever, and person-to-person transmission of human monkeypox.

Keywords

Branching processpower series familyextinctiongeneration distributionmaximum likelihood estimationepidemic model

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 62M05: Markov processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 771 - 779
Copyright
Copyright © Applied Probability Trust 1999 

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