Gómez-Corral, A, López-García, M, Lopez-Herrero, MJ et al. (1 more author) (2020) On First-Passage Times and Sojourn Times in Finite QBD Processes and Their Applications in Epidemics. Mathematics, 8 (10). 1718. ISSN 2227-7390
Abstract
In this paper, we revisit level-dependent quasi-birth-death processes with finitely many possible values of the level and phase variables by complementing the work of Gaver, Jacobs, and Latouche (Adv. Appl. Probab. 1984), where the emphasis is upon obtaining numerical methods for evaluating stationary probabilities and moments of first-passage times to higher and lower levels. We provide a matrix-analytic scheme for numerically computing hitting probabilities, the number of upcrossings, sojourn time analysis, and the random area under the level trajectory. Our algorithmic solution is inspired from Gaussian elimination, which is applicable in all our descriptors since the underlying rate matrices have a block-structured form. Using the results obtained, numerical examples are given in the context of varicella-zoster virus infections.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | epidemic modeling; first-passage times; hitting probabilities; quasi-birth-death processes; sojourn times |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Nov 2020 13:32 |
Last Modified: | 11 Nov 2020 13:32 |
Status: | Published |
Publisher: | MDPI |
Identification Number: | 10.3390/math8101718 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:167805 |