Open Access
November 2014 Stochastic monotonicity and continuity properties of functions defined on Crump–Mode–Jagers branching processes, with application to vaccination in epidemic modelling
Frank Ball, Miguel González, Rodrigo Martínez, Maroussia Slavtchova-Bojkova
Bernoulli 20(4): 2076-2101 (November 2014). DOI: 10.3150/13-BEJ551

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

Download Citation

Frank Ball. Miguel González. Rodrigo Martínez. Maroussia Slavtchova-Bojkova. "Stochastic monotonicity and continuity properties of functions defined on Crump–Mode–Jagers branching processes, with application to vaccination in epidemic modelling." Bernoulli 20 (4) 2076 - 2101, November 2014. https://doi.org/10.3150/13-BEJ551

Information

Published: November 2014
First available in Project Euclid: 19 September 2014

zbMATH: 1329.60299
MathSciNet: MR3263099
Digital Object Identifier: 10.3150/13-BEJ551

Keywords: coupling , general branching process , Monte-Carlo method , mumps in Bulgaria , SIR epidemic model , time to extinction , vaccination policies

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

Vol.20 • No. 4 • November 2014
Back to Top