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Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System

Department of Mathematics and Computer Sciences, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, Casablanca 20000, Morocco
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Math. Comput. Appl. 2018, 23(4), 52; https://doi.org/10.3390/mca23040052
Received: 7 September 2018 / Revised: 22 September 2018 / Accepted: 22 September 2018 / Published: 24 September 2018
(This article belongs to the Special Issue Optimization in Control Applications)
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Abstract

We consider a discrete-time susceptible-infected-removed-susceptible “again” (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible population. In addition, we define a new compartment, which models the dynamics of the number of controlled individuals and who are supposed not to be able to reach a long-term immunity due to the limited effect of control. Furthermore, we treat the resolution of this optimal control problem when there is a restriction on the number of susceptible people who have been controlled along the time of the control strategy. Further, we provide sufficient and necessary conditions for the existence of the sought optimal control, whose characterization is also given in accordance with an isoperimetric constraint. Finally, we present the numerical results obtained, using a computational method, which combines the secant method with discrete progressive-regressive schemes for the resolution of the discrete two-point boundary value problem. View Full-Text
Keywords: discrete-time model; SIRS model; optimal control; isoperimetric problem discrete-time model; SIRS model; optimal control; isoperimetric problem
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El Kihal, F.; Abouelkheir, I.; Rachik, M.; Elmouki, I. Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System. Math. Comput. Appl. 2018, 23, 52.

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