As of November 14, 2020, the number of people infected with the COVID-19 disease has reached more than 54 million people worldwide and more than 1323196 people have died, according to the World Health Organization. This requires many countries to impose a health emergency or quarantine, which has had positive results in reducing the spread of the COVID-19 pandemic, and it has also had negative economic, social and health effects. So, we suggest a mathematical model for the dynamics of how COVID-19 disease is spread, as well as a mathematical modeling for the dynamics of diabetes, then highlight the negative effect of quarantine has on the health of diabetics. 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.

Highlights We propose to study an optimal control approach with delay in state and control variables. Numerical simulation of different strategies. The cost of effectivness.

Nowadays, Diabetes is one of the most common diseases, which has a huge and growing socio-economic burden affecting individuals, families, and the whole society. In this paper, we propose an optimal control approach modeling the evolution from pre-diabetes to diabetes with and without complications and the effect of living environment. We show the existence of an optimal control and then use a numerical implicit finite-difference method to monitor the size of population in each compartment.

In this article, we study the transmission of COVID-19 in the human population, notably between potential people and infected people of all age groups. Our objective is to reduce the number of infected people, in addition to increasing the number of individuals who recovered from the virus and are protected. We propose a mathematical model with control strategies using two variables of controls that represent respectively, the treatment of patients infected with COVID-19 by subjecting them to quarantine within hospitals and special places and using masks to cover the sensitive body parts. Pontryagin’s Maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Finally, numerical simulations are presented with controls and without controls. Our results indicate that the implementation of the strategy that combines all the control variables adopted by the World Health Organization (WHO), produces excellent results similar to those achieved on the ground in Morocco.

We propose an optimal control strategy by conducting awareness campaigns for diabetics about the severity of complications of diabetes and the negative impact of an unbalanced lifestyle and the surrounding environment, as well as treatment and psychological follow-up. 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.