Person: Taipe Hidalgo, Diana Paulina
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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.
Uso del cine y otros medios audiovisuales como herramienta en la docencia de Matemáticas y Estadística
2024-06-25, Cabrera Gómez, Gloria, Gamboa Pérez, María, Mateo Navas, Luis Miguel, Monge Romojaro; Mireya, Pérez Pérez, Teresa, Pons Bordería, María Jesús, Susi García, María Del Rosario, Taipe Hidalgo, Diana Paulina, Cabrera Gómez, Gloria
El presente proyecto de innovación docente tiene como objetivo utilizar imágenes, podcasts, vídeos, canciones, cortes de películas, series de televisión, prensa digital, programa de radio o mensajes en redes sociales, en los que aparezcan contenidos matemáticos o estadísticos e insertarlos de manera dinámica en el desarrollo de la clase con el fin de mejorar la motivación, atención y aprendizaje.
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.