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

Ball, Frank; Gonz�lez, Miguel; Mart�nez, Rodrigo; Slavtchova-Bojkova, Maroussia

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.

Citation

Ball, F., González, M., Martínez, R., & Slavtchova-Bojkova, M. (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), https://doi.org/10.3150/13-BEJ551

• Journal Article Type: Article
• Acceptance Date: Jul 23, 2013
• Publication Date: Oct 1, 2014
• Deposit Date: Jun 20, 2016
• Publicly Available Date: Jun 20, 2016
• Journal: Bernoulli
• Print ISSN: 1350-7265
• Electronic ISSN: 1573-9759
• Publisher: Bernoulli Society for Mathematical Statistics and Probability
• Peer Reviewed: Peer Reviewed
• Volume: 20
• Issue: 4
• DOI: https://doi.org/10.3150/13-BEJ551
• Keywords: coupling; general branching process; Monte-Carlo method; mumps in Bulgaria; SIR epidemic model; time to extinction; vaccination policies
• Public URL: https://nottingham-repository.worktribe.com/output/994182
• Publisher URL: http://projecteuclid.org/euclid.bj/1411134454
• Contract Date: Jun 20, 2016