Some new mathematical models of the fractional-order system of human immune against IAV infection
Fractional derivative operators of non-integer order can be utilized as a powerful tool to model nonlinear fractional differential equations. In this paper, we propose numerical solutions for simulating fractional-order derivative operators with the power-law and exponential-law kernels. We construc...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2020268?viewType=HTML |
| _version_ | 1818733338572095488 |
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| author | H. M. Srivastava Khaled M. Saad J. F. Gómez-Aguilar Abdulrhman A. Almadiy |
| author_facet | H. M. Srivastava Khaled M. Saad J. F. Gómez-Aguilar Abdulrhman A. Almadiy |
| author_sort | H. M. Srivastava |
| collection | DOAJ |
| description | Fractional derivative operators of non-integer order can be utilized as a powerful tool to model nonlinear fractional differential equations. In this paper, we propose numerical solutions for simulating fractional-order derivative operators with the power-law and exponential-law kernels. We construct the numerical schemes with the help the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation. These schemes are applied to simulate the dynamical fractional-order model of the immune response (FMIR) to the uncomplicated influenza A virus (IAV) infection, which focuses on the control of the infection by the innate and adaptive immunity. Numerical results are then presented to show the applicability and efficiency on the FMIR. |
| first_indexed | 2024-12-17T23:47:53Z |
| format | Article |
| id | doaj.art-6e5b9dfa675143c69144f8e2ef68045b |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-17T23:47:53Z |
| publishDate | 2020-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-6e5b9dfa675143c69144f8e2ef68045b2022-12-21T21:28:15ZengAIMS PressMathematical Biosciences and Engineering1551-00182020-07-011754942496910.3934/mbe.2020268Some new mathematical models of the fractional-order system of human immune against IAV infectionH. M. Srivastava0Khaled M. Saad1J. F. Gómez-Aguilar2Abdulrhman A. Almadiy 31. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada 2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, China 3. Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan4. Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Kingdom of Saudi Arabia 5. Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen6. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C. P. 62490, Cuernavaca Morelos, México7. Department of Biology, College of Arts and Sciences, Najran University, Najran, Kingdom of Saudi ArabiaFractional derivative operators of non-integer order can be utilized as a powerful tool to model nonlinear fractional differential equations. In this paper, we propose numerical solutions for simulating fractional-order derivative operators with the power-law and exponential-law kernels. We construct the numerical schemes with the help the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation. These schemes are applied to simulate the dynamical fractional-order model of the immune response (FMIR) to the uncomplicated influenza A virus (IAV) infection, which focuses on the control of the infection by the innate and adaptive immunity. Numerical results are then presented to show the applicability and efficiency on the FMIR.https://www.aimspress.com/article/doi/10.3934/mbe.2020268?viewType=HTMLdynamical fractional-order model of immune response (fmir)lagrange polynomial interpolationinfluenza a virus (iav) |
| spellingShingle | H. M. Srivastava Khaled M. Saad J. F. Gómez-Aguilar Abdulrhman A. Almadiy Some new mathematical models of the fractional-order system of human immune against IAV infection Mathematical Biosciences and Engineering dynamical fractional-order model of immune response (fmir) lagrange polynomial interpolation influenza a virus (iav) |
| title | Some new mathematical models of the fractional-order system of human immune against IAV infection |
| title_full | Some new mathematical models of the fractional-order system of human immune against IAV infection |
| title_fullStr | Some new mathematical models of the fractional-order system of human immune against IAV infection |
| title_full_unstemmed | Some new mathematical models of the fractional-order system of human immune against IAV infection |
| title_short | Some new mathematical models of the fractional-order system of human immune against IAV infection |
| title_sort | some new mathematical models of the fractional order system of human immune against iav infection |
| topic | dynamical fractional-order model of immune response (fmir) lagrange polynomial interpolation influenza a virus (iav) |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2020268?viewType=HTML |
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