Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling
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 v...
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| Format: | Article |
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Bernoulli Society for Mathematical Statistics and Probability
2014
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| Online Access: | https://eprints.nottingham.ac.uk/34196/ |
| _version_ | 1848794796204752896 |
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| author | Ball, Frank González, Miguel Martínez, Rodrigo Slavtchova-Bojkova, Maroussia |
| author_facet | Ball, Frank González, Miguel Martínez, Rodrigo Slavtchova-Bojkova, Maroussia |
| author_sort | Ball, Frank |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:21:53Z |
| format | Article |
| id | nottingham-34196 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:21:53Z |
| publishDate | 2014 |
| publisher | Bernoulli Society for Mathematical Statistics and Probability |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-341962020-05-04T20:13:06Z https://eprints.nottingham.ac.uk/34196/ Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling Ball, Frank González, Miguel Martínez, Rodrigo Slavtchova-Bojkova, Maroussia 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. Bernoulli Society for Mathematical Statistics and Probability 2014-10 Article PeerReviewed Ball, Frank, González, Miguel, 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 coupling; general branching process; Monte-Carlo method; mumps in Bulgaria; SIR epidemic model; time to extinction; vaccination policies http://projecteuclid.org/euclid.bj/1411134454 doi:10.3150/13-BEJ551 doi:10.3150/13-BEJ551 |
| spellingShingle | coupling; general branching process; Monte-Carlo method; mumps in Bulgaria; SIR epidemic model; time to extinction; vaccination policies 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 |
| title | Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling |
| title_full | Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling |
| title_fullStr | Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling |
| title_full_unstemmed | Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling |
| title_short | Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling |
| title_sort | stochastic monotonicity and continuity properties of functions defined on crump-mode-jagers branching processes, with application to vaccination in epidemic modelling |
| topic | coupling; general branching process; Monte-Carlo method; mumps in Bulgaria; SIR epidemic model; time to extinction; vaccination policies |
| url | https://eprints.nottingham.ac.uk/34196/ https://eprints.nottingham.ac.uk/34196/ https://eprints.nottingham.ac.uk/34196/ |