## Artigo

• Similares em SciELO

## versão impressa ISSN 1409-2433

### Rev. Mat vol.28 no.1 San José Jan./Jul. 2021

#### http://dx.doi.org/10.15517/rmta.v28i1.42077

Artículo

Optimizing the quarantine cost for suppression of the COVID-19 epidemic in México

Optimización del costo de la cuarentena para la supresión de la epidemia del COVID-19 en México

1Universidad Michoacana de San Nicolás de Hidalgo; Institute of Physics and Mathematics; Morelia; México; abdon.choque@umich.mx

2Lomonosov Moscow State University; Faculty of Computational Mathematics and Cybernetics; Moscow; Russia; khailov@cs.msu.su

3Texas Woman’s University; Department of Mathematics and Computer Sciences; Denton; United States; egrigorieva@twu.edu

Abstract

This paper is one of the few attempts to use the optimal control theory to find optimal quarantine strategies for eradication of the spread of the COVID-19 infection in the Mexican human population. This is achieved by introducing into the SEIR model a bounded control function of time that reflects these quarantine measures. The objective function to be minimized is the weighted sum of the total infection level in the population and the total cost of the quarantine. An optimal control problem reflecting the search for an effective quarantine strategy is stated and solved analytically and numerically. The properties of the corresponding optimal control are established analytically by applying the Pontryagin maximum principle. The optimal solution is obtained numerically by solving the two-point boundary value problem for the maximum principle using MATLAB software. A detailed discussion of the results and the corresponding practical conclusions are presented.

Keywords: coronavirus; quarantine cost; Pontryagin maximum principal; optimal control.

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.

Palabras clave: coronavirus; costo de una cuarentena; principio del máximo de Pontryagin; control óptimo.

Mathematics Subject Classification: 49N90, 58E25, 92D25, 92D30

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Received: August 07, 2020; Revised: November 12, 2020; Accepted: November 12, 2020