Optimizing the quarantine cost for suppression of the Covid-19 epidemic in Mexico

• Autores: Abdon E. Choque Rivero, Evgenii N. Khailov, Ellina V. Grigorieva
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 28, Nº. 1, 2021, págs. 55-78
• Idioma: inglés
• DOI: 10.15517/rmta.v28i1.42077
• Títulos paralelos:
  • Optimización del costo de la cuarentena para la supresión de la epidemia del Covid-19en México
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    En este trabajo empleamos la teoría de control óptimo para encon-trar una cuarentena óptima y estrategias para la erradicación de la propa-gación de la infección por COVID-19 en la población humana mexicana.En un modelo SEIR, introducimos un control acotado que es una fun-ción respecto del tiempo, la cual refleja las medidas de la cuarentena. Lafunción objetivo a minimizar es la suma ponderada del nivel total de in-fección en la población y el costo total de la cuarentena. Planteamos unproblema de control óptimo que representa la búsqueda de una estrate-gia eficaz de una cuarentena. Resolvemos este problema analíticamente ynuméricamente. Establecemos analíticamente las propiedades del controlóptimo correspondiente aplicando el principio del máximo de Pontryagin.La solución óptima se obtiene resolviendo un problema de valor de fron-tera de dos puntos asociado al principio del máximo. Usamos el softwareMATLAB. Presentamos una discusión detallada de los resultados y lascorrespondientes conclusiones prácticas

  • English

    This paper is one of the few attempts to use the optimal control theoryto find optimal quarantine strategies for eradication of the spread of theCOVID-19 infection in the Mexican human population. This is achievedby introducing into the SEIR model a bounded control function of timethat reflects these quarantine measures. The objective function to be min-imized is the weighted sum of the total infection level in the populationand the total cost of the quarantine. An optimal control problem reflectingthe search for an effective quarantine strategy is stated and solved analyti-cally and numerically. The properties of the corresponding optimal controlare established analytically by applying the Pontryagin maximum princi-ple. The optimal solution is obtained numerically by solving the two-pointboundary value problem for the maximum principle using MATLAB soft-ware. A detailed discussion of the results and the corresponding practicalconclusions are presented.

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