Gómez Corral, AntonioLópez-García, M.López Herrero, María JesúsTaipe Hidalgo, Diana Paulina2024-03-082024-03-082020-10Gómez-Corral, A. et al. (2020) «On first-passage times and sojourn times in finite qbd processes and their applications in epidemics», Mathematics, 8(10), pp. 1-26. doi:10.3390/MATH8101718.2227-739010.3390/math8101718https://hdl.handle.net/20.500.14352/102080In 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.3390/math8101718https://www.mdpi.com/2227-7390/8/10/1718open access519.21519.22-76616.9Epidemic modelingFirst-passage timesHitting probabilitiesQuasi-birth-death processesSojourn timesProbabilidades (Estadística)Ciencias BiomédicasEnfermedades infecciosas3202 Epidemiología2404.01 Bioestadística1208 Probabilidad3205.05 Enfermedades Infecciosas