Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case study of Brazil and cost-effectiveness

Abdelfatah Kouidere; Driss Kada; Omar Balatif; Mostafa Rachik; Mouhcine Naim

doi:10.1016/j.chaos.2020.110438

Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case study of Brazil and cost-effectiveness

Chaos Solitons Fractals. 2021 Jan:142:110438. doi: 10.1016/j.chaos.2020.110438. Epub 2020 Nov 4.

Authors

Abdelfatah Kouidere¹, Driss Kada², Omar Balatif³, Mostafa Rachik¹, Mouhcine Naim¹

Affiliations

¹ LAMS, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan II University of Casablanca, Morocco.
² Laboratory of Information Technology and Modeling, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan II University, Casablanca, Morocco.
³ Laboratory of Dynamical Systems, Mathematical Engineering Team (INMA), Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco.

Abstract

As of June 02, 2020. The number of people infected with COVID-19 virus in Brazil was about 529,405, the number of death is 30046, the number of recovered is 211080, and the number is subject to increase. This is due to the delay by a number of countries in general, and Brazil in particular, in taking preventive and proactive measures to limit the spread of the COVID-19 pandemic. So, we propose to study an optimal control approach with delay in state and control variables in our mathematical model proposed by kouidere et al. which describes the dynamics of the transmission of the COVID-19. That the time with delay represent the delay to applying preventive precautions measures. Pontryagin's maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using MATLAB.

Keywords: COVID-19; Mathematical modeling; Optimal control with delay; SARS-CoV-2.