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.

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.