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A fractional numerical study on a chronic hepatitis C virus infection model with immune response

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  • Saad, Khaled M.
  • Gómez-Aguilar, J.F.
  • Almadiy, Abdulrhman A.

Abstract

Our main aim in this article is to introduce and investigate a new model of fractional-order model for hepatitis C virus (HCV) infection with immune response, in which the effect of dendritic cells (DC) and cytotoxic T lymphocytes (CTL) on HCV infection is considered. In the first stage, the HCV model was extended to Liouville-Caputo (LC) fractional derivative and Caputo-Fabrizio fractional derivative in the Caputo sense (CFC). In particular, we evaluate the approximate solutions of this model by means of the power law and the exponential law kernel. The approximate solutions are based upon the fundamental theorem of fractional calculus as well as the Lagrange polynomial interpolation. We study the effect of the variation the fractional-order on the behavior of the solutions due to the presence of definitions of new fractional-calculus operators. We observe that the chaotic behavior and illustrate the chaotic of a chronic HCV infection model with immune response by plotting the solutions in the plane. Finally, some numerical simulations using with the aid of Mathematica were done for different values of fractional order.

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  • Saad, Khaled M. & Gómez-Aguilar, J.F. & Almadiy, Abdulrhman A., 2020. "A fractional numerical study on a chronic hepatitis C virus infection model with immune response," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304598
    DOI: 10.1016/j.chaos.2020.110062
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    References listed on IDEAS

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    1. M. M. Khader & Khaled. M. Saad, 2020. "Numerical treatment for studying the blood ethanol concentration systems with different forms of fractional derivatives," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-13, January.
    2. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
    3. Taneco-Hernández, M.A. & Morales-Delgado, V.F. & Gómez-Aguilar, J.F., 2019. "Fractional Kuramoto–Sivashinsky equation with power law and stretched Mittag-Leffler kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    4. Jajarmi, Amin & Arshad, Sadia & Baleanu, Dumitru, 2019. "A new fractional modelling and control strategy for the outbreak of dengue fever," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    5. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    6. Saad, Khaled M. & Srivastava, H.M. & Gómez-Aguilar, J.F., 2020. "A Fractional Quadratic autocatalysis associated with chemical clock reactions involving linear inhibition," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    7. Galeone, Luciano & Garrappa, Roberto, 2008. "Fractional Adams–Moulton methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1358-1367.
    8. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    9. Goswami, Amit & Singh, Jagdev & Kumar, Devendra & Sushila,, 2019. "An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 563-575.
    10. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    11. Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Saad, Khaled M. & Khan, Muhammad Altaf & Agarwal, P., 2019. "Analytic solution for oxygen diffusion from capillary to tissues involving external force effects: A fractional calculus approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 48-65.
    12. BİLDİK, Necdet & DENİZ, Sinan & SAAD, Khaled M., 2020. "A comparative study on solving fractional cubic isothermal auto-catalytic chemical system via new efficient technique," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
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