Journal of Applied Probability

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

C. P. Farrington and A. D. Grant

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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.

Article information

Source
J. Appl. Probab. Volume 36, Number 3 (1999), 771-779.

Dates
First available: 18 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.jap/1032374633

Digital Object Identifier
doi:10.1239/jap/1032374633

Mathematical Reviews number (MathSciNet)
MR1737052

Zentralblatt MATH identifier
0953.60077

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 62M05: Markov processes: estimation

Keywords
Branching process power series family extinction generation distribution maximum likelihood estimation epidemic model

Citation

Farrington, C. P.; Grant, A. D. The distribution of time to extinction in subcritical branching processes: applications to outbreaks of infectious disease. Journal of Applied Probability 36 (1999), no. 3, 771--779. doi:10.1239/jap/1032374633. http://projecteuclid.org/euclid.jap/1032374633.


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