Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains.
| Autor: | Sweilam NH; Cairo University, Faculty of Science, Mathematics Department, 12613 Giza, Egypt., Al-Mekhlafi SM; Sana'a University, Faculty of Education, Mathematics Department, Sana'a, Yemen., Baleanu D; Cankaya University, Department of Mathematics, 06530, Ankara, Turkey.; Institute of Space Sciences, P.O. Box MG 23, Magurele, 077125 Bucharest, Romania. |
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| Jazyk: | angličtina |
| Zdroj: | Journal of advanced research [J Adv Res] 2019 Jan 19; Vol. 17, pp. 125-137. Date of Electronic Publication: 2019 Jan 19 (Print Publication: 2019). |
| DOI: | 10.1016/j.jare.2019.01.007 |
| Abstrakt: | The objective of this paper is to study the optimal control problem for the fractional tuberculosis (TB) infection model including the impact of diabetes and resistant strains. The governed model consists of 14 fractional-order (FO) equations. Four control variables are presented to minimize the cost of interventions. The fractional derivative is defined in the Atangana-Baleanu-Caputo (ABC) sense. New numerical schemes for simulating a FO optimal system with Mittag-Leffler kernels are presented. These schemes are based on the fundamental theorem of fractional calculus and Lagrange polynomial interpolation. We introduce a simple modification of the step size in the two-step Lagrange polynomial interpolation to obtain stability in a larger region. Moreover, necessary and sufficient conditions for the control problem are considered. Some numerical simulations are given to validate the theoretical results. |
| Databáze: | MEDLINE |
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