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Nonlinearly perturbed birth-death-type models
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-2626-5598
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2018 (English)In: Stochastic Processes and Applications: SPAS2017, Västerås and Stockholm, Sweden, October 4–6, 2017 / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, Cham: Springer , 2018, p. 189-244Chapter in book (Refereed)
Abstract [en]

Asymptotic expansions are presented for stationary and conditional quasi-stationary distributions of nonlinearly perturbed birth-death-type semi-Markov models, as well as algorithms for computing the coefficients of these expansions. Three types of applications are discussed in detail. The first is a model of population growth, where either an isolated population is perturbed by immigration, or a sink population with immigration is perturbed by internal births. The second application is epidemic spread of disease, in which a closed population is perturbed by infected individuals from outside. The third model captures the time dynamics of the genetic composition of a population with genetic drift and selection, that is perturbed by various mutation scenarios.

Place, publisher, year, edition, pages
Cham: Springer , 2018. p. 189-244
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009, E-ISSN 2194-1017 ; 271
Keywords [en]
Semi-Markov birth-death process, Quasi-stationary distribution, Nonlinear perturbation, Population dynamics model, Population genetics model, Epidemic model
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-165105DOI: 10.1007/978-3-030-02825-1_11ISBN: 978-3-030-02824-4 (print)ISBN: 978-3-030-02825-1 (electronic)OAI: oai:DiVA.org:su-165105DiVA, id: diva2:1281234
Available from: 2019-01-21 Created: 2019-01-21 Last updated: 2019-01-31Bibliographically approved

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  • apa
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