Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling

Ball, Frank and González, Miguel and Martínez, Rodrigo and Slavtchova-Bojkova, Maroussia (2014) Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling. Bernoulli, 20 (4). pp. 2076-2101. ISSN 1573-9759

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Abstract

This paper is concerned with Crump-Mode-Jagers branching processes, describing spread of an epidemic depending on the proportion of the population that is vaccinated. Births in the branching process are aborted independently with a time-dependent probability given by the fraction of the population vaccinated. Stochastic monotonicity and continuity results for a wide class of functions (e.g., extinction time and total number of births over all time) defined on such a branching process are proved using coupling arguments, leading to optimal vaccination schemes to control corresponding functions (e.g., duration and final size) of epidemic outbreaks. The theory is illustrated by applications to the control of the duration of mumps outbreaks in Bulgaria.

Item Type: Article
Keywords: coupling; general branching process; Monte-Carlo method; mumps in Bulgaria; SIR epidemic model; time to extinction; vaccination policies
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.3150/13-BEJ551
Depositing User: Ball, Prof Frank Granville
Date Deposited: 20 Jun 2016 08:52
Last Modified: 16 Sep 2016 03:10
URI: http://eprints.nottingham.ac.uk/id/eprint/34196

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