Archivos suplementarios
Palabras clave
quarantine cost
Pontryagin maximum principal
optimal control
coronavirus
costo de una cuarentena
principio del máximo de Pontryagin
control óptimo
Cómo citar
Resumen
En este trabajo empleamos la teoría de control óptimo para encontrar una cuarentena óptima y estrategias para la erradicación de la propagación de la infección por COVID-19 en la población humana mexicana. En un modelo SEIR, introducimos un control acotado que es una función respecto del tiempo, la cual refleja las medidas de la cuarentena. La función objetivo a minimizar es la suma ponderada del nivel total de infección en la población y el costo total de la cuarentena. Planteamos un problema de control óptimo que representa la búsqueda de una estrategia eficaz de una cuarentena. Resolvemos este problema analíticamente y numéricamente. Establecemos analíticamente las propiedades del control óptimo correspondiente aplicando el principio del máximo de Pontryagin. La solución óptima se obtiene resolviendo un problema de valor de frontera de dos puntos asociado al principio del máximo. Usamos el software MATLAB. Presentamos una discusión detallada de los resultados y las correspondientes conclusiones prácticas.
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