A multi-region discrete time mathematical modeling of the dynamics of Covid-19 virus propagation using optimal control
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A multi-region discrete time mathematical modeling of the dynamics of Covid-19 virus propagation using optimal control Bouchaib Khajji1
· Driss Kada2 · Omar Balatif3 · Mostafa Rachik1
Received: 1 March 2020 © Korean Society for Informatics and Computational Applied Mathematics 2020
Abstract We study in this work a discrete mathematical model that describes the dynamics of transmission of the Corona virus between humans on the one hand and animals on the other hand in a region or in different regions. Also, we propose an optimal strategy to implement the optimal campaigns through the use of awareness campaigns in region j that aims at protecting individuals from being infected by the virus, security campaigns and health measures to prevent the movement of individuals from one region to another, encouraging the individuals to join quarantine centers and the disposal of infected animals. The aim is to maximize the number of individuals subjected to quarantine and trying to reduce the number of the infected individuals and the infected animals. Pontryagin’s maximum principle in discrete time is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using Matlab. The Incremental Cost-Effectiveness Ratio was calculated to investigate the cost-effectiveness of all possible combinations of the four control measures. Using cost-effectiveness analysis, we show that control of protecting susceptible individuals, preventing their contact with the infected individuals and encouraging the exposed individuals to join quarantine centers provides the most cost-effective strategy to control the disease. Keywords Discrete mathematical model · Multi-regions · Optimal control · Covid-19 · Cost-effective intervention Mathematics Subject Classification 93A30 · 49J15 · 65Q10 · 93C55
1 Introduction The new Corona Virus (Covid-19) appeared in Wuhan, China on September 31, 2019, where the World Health Organization has received multiple cases of pneumonia in
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this city. The characteristics of the virus did not match any known viruses. This new virus comes from a group of viruses that include those that cause common cold, SARS syndrome, and respiratory syndrome in the Middle East. This virus was temporarily called the emerging corona virus (Covid-19) [1]. This virus took several forms and names, among them MERS-COV. It first appeared in 2012 in the Kingdom of Saudi Arabia and then in 2015 in South Korea and the number of people infected with this disease was high. These countries used the centers of treatment to control the spread of this disease along with other preventive measures. Some studies conducted in 2015 showed that 1046 patients were infected with the virus MERS-COV and cases of deaths reached 298 among which 67 cases were in the United Arab Emirates. In 2018, more than 500 camels died due to this disease in Saudi Arabia, but the number of deaths due
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