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Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman-Harris Branching Processes: An Application to Epidemic Modelling

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

M. González ,
R. Martínez  and
M. Slavtchova-Bojkova
M. González*
Affiliation:
University of Extremadura
R. Martínez*
Affiliation:
University of Extremadura
M. Slavtchova-Bojkova*
Affiliation:
Bulgarian Academy of Sciences
*
∗Postal address: Department of Mathematics, University of Extremadura, Badajoz 06006, Spain.
∗Postal address: Department of Mathematics, University of Extremadura, Badajoz 06006, Spain.
∗∗∗Postal address: Department of Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia 1113, Bulgaria.
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Abstract

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The aim of this paper is to study the stochastic monotonicity and continuity properties of the extinction time of Bellman-Harris branching processes depending on their reproduction laws. Moreover, we show their applications in an epidemiological context, obtaining an optimal criterion to establish the proportion of susceptible individuals in a given population that must be vaccinated in order to eliminate an infectious disease. First the spread of infection is modelled by a Bellman-Harris branching process. Finally, we provide a simulation-based method to determine the optimal vaccination policies.

Keywords

Bellman-Harris branching processextinction timevaccination policiesSIRMonte Carlo method

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 92D30: Epidemiology
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 58 - 71
Copyright
Copyright © Applied Probability Trust 2010 

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