Geodesic
Output trajectory controllability of a discrete-time sir epidemic model
Lahbib Benahmadi1 ; Mustapha Lhous1 ; Abdessamad TRIDANE2 ; Mostafa Rachik3
1 Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, B.P. 5366 Maarif Casablanca, Morocco
2 Department of Mathematical Sciences, United Arab Emirates University, Al-Ain PO Box 15551, UAE
3 Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Sidi Othman Casablanca B.P. 7955, Morocco
Mathematical modelling of natural phenomena, Tome 18 (2023), article no. 16 Cet article a éte moissonné depuis la source EDP Sciences

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Developing new approaches that help control the spread of infectious diseases is a critical issue for public health. Such approaches must consider the available resources and capacity of the healthcare system. In this paper, we present a new mathematical approach to controlling an epidemic model by investigating the optimal control that aims to bring the output of the epidemic to target a desired disease output yd = (ydi)i∈{0,...,N}. First, we use the state-space technique to transfer the trajectory controllability to optimal control with constraints on the final state. Then, we use the fixed point theorems to determine the set of admissible controls and solve the output trajectory controllability problem. Finally, we apply our method to the model of a measles epidemic, and we give a numerical simulation to illustrate the findings of our approach.
DOI : 10.1051/mmnp/2023015

Lahbib Benahmadi 1 ; Mustapha Lhous 1 ; Abdessamad TRIDANE 2 ; Mostafa Rachik 3

1 Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, B.P. 5366 Maarif Casablanca, Morocco
2 Department of Mathematical Sciences, United Arab Emirates University, Al-Ain PO Box 15551, UAE
3 Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Sidi Othman Casablanca B.P. 7955, Morocco 
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Lahbib Benahmadi; Mustapha Lhous; Abdessamad TRIDANE; Mostafa Rachik. Output trajectory controllability of a discrete-time sir epidemic model. Mathematical modelling of natural phenomena, Tome 18 (2023), article  no. 16. doi: 10.1051/mmnp/2023015

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