Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains
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 cos...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2019-05-01
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| Series: | Journal of Advanced Research |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090123219300062 |
| _version_ | 1818190037201715200 |
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| author | N.H. Sweilam S.M. AL-Mekhlafi D. Baleanu |
| author_facet | N.H. Sweilam S.M. AL-Mekhlafi D. Baleanu |
| author_sort | N.H. Sweilam |
| collection | DOAJ |
| description | 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. Keywords: Tuberculosis model, Diabetes and resistant strains, Atangana-Baleanu fractional derivative, Lagrange polynomial interpolation, Nonstandard two-step Lagrange interpolation method |
| first_indexed | 2024-12-11T23:52:20Z |
| format | Article |
| id | doaj.art-7064d5dc5dc540589a16d7d69eeacc66 |
| institution | Directory Open Access Journal |
| issn | 2090-1232 |
| language | English |
| last_indexed | 2024-12-11T23:52:20Z |
| publishDate | 2019-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Journal of Advanced Research |
| spelling | doaj.art-7064d5dc5dc540589a16d7d69eeacc662022-12-22T00:45:26ZengElsevierJournal of Advanced Research2090-12322019-05-0117125137Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strainsN.H. Sweilam0S.M. AL-Mekhlafi1D. Baleanu2Cairo University, Faculty of Science, Mathematics Department, 12613 Giza, Egypt; Corresponding author.Sana'a University, Faculty of Education, Mathematics Department, Sana'a, YemenCankaya University, Department of Mathematics, 06530, Ankara, Turkey; Institute of Space Sciences, P.O. Box MG 23, Magurele, 077125 Bucharest, RomaniaThe 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. Keywords: Tuberculosis model, Diabetes and resistant strains, Atangana-Baleanu fractional derivative, Lagrange polynomial interpolation, Nonstandard two-step Lagrange interpolation methodhttp://www.sciencedirect.com/science/article/pii/S2090123219300062 |
| spellingShingle | N.H. Sweilam S.M. AL-Mekhlafi D. Baleanu Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains Journal of Advanced Research |
| title | Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains |
| title_full | Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains |
| title_fullStr | Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains |
| title_full_unstemmed | Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains |
| title_short | Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains |
| title_sort | optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains |
| url | http://www.sciencedirect.com/science/article/pii/S2090123219300062 |
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