Taipe Hidalgo, Diana Paulina

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First Name
Diana Paulina
Last Name
Taipe Hidalgo
Universidad Complutense de Madrid
Faculty / Institute
Estudios estadísticos
Estadística y Ciencia de los Datos
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A Markovian epidemic model in a resource-limited environment

2023-08-02, Gómez Corral, Antonio, López Herrero, María Jesús, Taipe Hidalgo, Diana Paulina

In this paper, we present a Markov chain model to study infectious disease outbreaks assuming that healthcare facilities, specifically the number of hospital beds for infected individuals, are limited. Therefore, only a restricted number of infected individuals can be admitted to a hospital ward and receive medical care at the same time. Since the pathogen spreads both inside and outside the ward, modeling the dynamics of the epidemic involves SIS- and SI-type models that are inherently linked to each other, in such a way that the potential transmission of the pathogen outside the ward is only possible when the hospital ward is working functionally full. Our goal is to study the influence of the resource-limited environment on performance measures related to hospital operations, such as the time until the ward reaches its maximum capacity, the number of critical events —occurring when the hospital ward reaches its maximum capacity—, the time that limited healthcare facilities should be continuously active, or the economic impact of administering therapeutic treatments, which could be evaluated in terms of the number of admissions and the number of treatments provided in the case of reinfection.

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On first-passage times and sojourn times in finite qbd processes and their applications in epidemics

2020-10, Gómez Corral, Antonio, López-García, M., López Herrero, María Jesús, Taipe Hidalgo, Diana Paulina

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.