# Mathematical modeling and optimal control strategy for the monkeypox epidemic

2023;
: pp. 944–955

Revised: June 25, 2023
Accepted: June 27, 2023
1
Laboratory LMACS, Sultan Moulay Slimane University, MATIC research team: Applied Mathematics and Information and Communication Technologies, Department of Mathematics and Computer Science, Khouribga Polydisciplinary Faculty, Morocco
2
Laboratory LMACS, Sultan Moulay Slimane University, MATIC research team: Applied Mathematics and Information and Communication Technologies, Department of Mathematics and Computer Science, Khouribga Polydisciplinary Faculty, Morocco
3
Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan II University of Casablanca, Morocco
4
Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sik, Hassan II University of Casablanca, Morocco
5
Laboratory LMACS, Sultan Moulay Slimane University, MATIC research team: Applied Mathematics and Information and Communication Technologies, Department of Mathematics and Computer Science, Khouribga Polydisciplinary Faculty, Morocco

In this study, we propose a discrete time mathematical model (SEIQR) that describes the dynamics of monkeypox within a human population.  The studied population is divided into five compartments: susceptible ($S$), exposed ($E$), infected ($I$), quarantined ($Q$), and recovered ($R$).  Also, we propose an optimal strategy to fight against the spread of this epidemic.  In this sense we use three controls which represent: 1) the awarness of vulnerable people through the media, civil society and education; 2) the quarantine of infected persons at home or, if required, in hospital; 3) encouraging of vaccination of susceptible persons.  To characterize these optimal controls, we apply the Pontryagin's maximum principle.  The optimality system is solved numerically using Matlab.  Therefore, the obtained results confirm the effectiveness of the proposed optimization approach.

Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 944–955 (2023)