Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
Control óptimo de orden fraccionario para un modelo de eficacia del tratamiento de la tuberculosis con presencia de VIH/Sida y diabetes
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Palabras clave

Diabetes
HIV/AIDS
fractional derivatives in the Caputo sense
optimal control problem
tuberculosis
diabetes
VIH/SIDA
derivadas fraccionarias en el sentido de Caputo
problema de control óptimo
tuberculosis

Cómo citar

Delgado-Moya, E., & Pietrus, A. (2022). Control óptimo de orden fraccionario para un modelo de eficacia del tratamiento de la tuberculosis con presencia de VIH/Sida y diabetes. Revista De Matemática: Teoría Y Aplicaciones, 29(2), 177–223. https://doi.org/10.15517/rmta.v29i2.50888

Resumen

En este trabajo, aprovechando las ventajas del uso de las derivadas de orden fraccionario en el sentido de Caputo, presentamos un estudio de control óptimo de la eficacia del tratamiento de la tuberculosis (TB) en presencia del VIH/SIDA y la diabetes. El modelo matemático que es controlado se encuentra en [17] y estudia la relación entre la tuberculosis, el VIH/SIDA y la diabetes con respecto a la eficacia del tratamiento y diferencia en tuberculosis multirresistente (TB-MDR), y tuberculosis extremadamente resistente (TB-XDR). La definición de los controles se centra en evitar la reinfección/reactivación, la TB-MDR y la TB-XDR en las diferentes subpoblaciones (TB únicamente, TB-VIH/SIDA y TB-Diabetes). El modelo dividido en subpoblaciones nos permite diferenciar los comportamientos de la transmisión y la resistencia y evaluar los diferentes costos en la aplicación de los controles. Realizamos simulaciones computacionales con datos de la literatura para estudiar nuestro problema de control en un escenario específico. Exploramos el comportamiento del número básico de reproducción variando la tasa de contacto efectivo y los parámetros asociados a la resistencia para diferentes valores de _ (orden fraccional). Estudiamos diferentes estrategias de control basadas en la activación de los controles y encontramos que la más efectiva es cuando activamos todos los controles. Con esta estrategia, reducimos el número de casos resistentes, principalmente en la TB-XDR en diabéticos que tiene un fuerte impacto en la dinámica de resistencia y transmisión de la tuberculosis. Además, esta estrategia evita el crecimiento futuro del número de casos resistentes.

https://doi.org/10.15517/rmta.v29i2.50888
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DVI

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