On first-passage times and sojourn times in finite qbd processes and their applications in epidemics
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 stationa...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/102080 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/102080 |
| Access Level: | acceso abierto |
| Palavra-chave: | 519.21 519.22-76 616.9 Epidemic modeling First-passage times Hitting probabilities Quasi-birth-death processes Sojourn times Probabilidades (Estadística) Ciencias Biomédicas Enfermedades infecciosas 3202 Epidemiología 2404.01 Bioestadística 1208 Probabilidad 3205.05 Enfermedades Infecciosas |
| Resumo: | 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. |
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