## Bernoulli

• Bernoulli
• Volume 20, Number 4 (2014), 2076-2101.

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

#### 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.

#### Article information

Source
Bernoulli, Volume 20, Number 4 (2014), 2076-2101.

Dates
First available in Project Euclid: 19 September 2014

https://projecteuclid.org/euclid.bj/1411134454

Digital Object Identifier
doi:10.3150/13-BEJ551

Mathematical Reviews number (MathSciNet)
MR3263099

Zentralblatt MATH identifier
1329.60299

#### Citation

Ball, Frank; González, Miguel; Martínez, Rodrigo; Slavtchova-Bojkova, Maroussia. Stochastic monotonicity and continuity properties of functions defined on Crump–Mode–Jagers branching processes, with application to vaccination in epidemic modelling. Bernoulli 20 (2014), no. 4, 2076--2101. doi:10.3150/13-BEJ551. https://projecteuclid.org/euclid.bj/1411134454

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