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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., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2021 Elsevier Ltd. All rights reserved.)

The aim of this study is to model the transmission of COVID-19 and investigate the impact of some control strategies on its spread. We propose an extension of the classical SEIR model, which takes into account the age structure and uses fractional-order derivatives to have a more realistic model. For each age group j the population is divided into seven classes namely susceptible S j , exposed E j , infected with high risk I h j , infected with low risk I l j , hospitalized H j , recovered with and without psychological complications R 1 j and R 2 j , respectively. In our model, we incorporate three control variables which represent: awareness campaigns, diagnosis and psychological follow-up. The purpose of our control strategies is protecting susceptible individuals from being infected, minimizing the number of infected individuals with high and low risk within a given age group j , as well as reducing the number of recovered individuals with psychological complications. Pontryagin's maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. Numerical simulations performed using Matlab, are provided to show the effectiveness of three control strategies and the effect of the order of fractional derivative on the efficiency of these control strategies. Using a cost-effectiveness analysis method, our results show that combining awareness with diagnosis is the most effective strategy. To the best of our knowledge, this work is the first that propose a framework on the control of COVID-19 transmission based on a multi-age model with Caputo time-fractional derivative., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2020 Elsevier Ltd. All rights reserved.)

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., Competing Interests: The authors declare that they have no conflict of interests., (© 2020 Elsevier Ltd. All rights reserved.)

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., Competing Interests: The authors declare that they have no conflicts of interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2020 Elsevier Ltd. All rights reserved.)