A spatiotemporal spread of COVID-19 pandemic with vaccination optimal control strategy: A case study in Morocco

On March 2, 2020, the Moroccan Ministry of Health announced the first case of COVID-19 in the city of Casablanca for a Moroccan tourist who came from Italy.  The SARS-COV-2 virus has spread throughout the Kingdom of Morocco.  In this paper, we study the spatiotemporal transmission of the COVID-19 virus in the Kingdom of Morocco.  By supporting a SI$_{\rm W}$IHR partial differential equation for the spread of the COVID-19 pandemic in Morocco as a case study.  Our main goal is to characterize the optimum order of controlling the spread of the COVID-19 pandemic by adopting a vaccination strategy, the aim of which is to reduce the number of susceptible and infected individuals without vaccination and to maximize the recovered individuals by reducing the cost of vaccination using one of the vaccines approved by the World Health Organization.  To do this, we proved the existence of a pair of control. It provides a description of the optimal controls in terms of state and auxiliary functions.  Finally, we provided numerical simulations of data related to the transmission of the COVID-19 pandemic.  Numerical results are presented to illustrate the effectiveness of the adopted approach.

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