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Fractional Calculus Model for the Hepatitis C with Different Types of Virus Genome

Received: 6 September 2016     Accepted: 18 September 2016     Published: 11 October 2016
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Abstract

In this paper, a fractional order model to study the spread of HCV-subtype 4a amongst the Egyptian population is constructed. The stability of the boundary and positive fixed points is studied. The generalized Adams-Bashforth-Moulton method is used to solve and simulate the system of fractional differential equations.

Published in International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 3)
DOI 10.11648/j.ijssam.20160103.12
Page(s) 23-29
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Hepatitis C Virus, Fractional Order, Stability, Numerical Method, Sovaldi

References
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[2] E. Ahmed, A. M. A. El-Sayed, H. A. A. El-Saka; On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rossler, Chua and Chen systems, Physics Letters A, 358 (2006), 1–4.
[3] E. Ahmed, A. M. A. El-Sayed, H. A. A. El-Saka; Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models, J. Math. Anal. Appl, 325 (2007), 542–553.
[4] R. M. Anderson; R. M. May; Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991.
[5] L. Debnath; Recent applications of fractional calculus to science and engineering. International Journal of Mathematics and Mathematical Sciences, 54 (2003) 3413–3442.
[6] K. Diethelm, N. J. Ford; Analysis of fractional differential equations, J Math Anal Appl, 256 (2002), 229–248.
[7] K. Diethelm, N. J. Ford, A.D. Freed; A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dyn, 29 (2002), 3–22.
[8] Y. Ding, H. Ye; A fractional-order differential equation model of HIV infection of CD4+T - Cells, Mathematical and Computer Modeling, 50 (2009), 386–392.
[9] Greenhalgh, D. and Moneim, I. A., 2003, SIRS epidemic model and simulations using different types of seasonal contact rate. Systems Analysis Modelling Simulation, May, 43 (5), 573-600.
[10] E. H. Elbasha, A. B. Gumel; Analyzing the dynamics of an SIRS vaccination model with waning natural and vaccine-induced immunity, Trends in Parasitology, 12 (2011), 2692–2705.
[11] M. Elshahed and A. Alsaedi; The Fractional SIRC Model and Influenza A, Mathematical Problems in Engineering, Article ID 480378 (2011), 1–9.
[12] M. Elshahed, F. Abd El-Naby; Fractional Calculus Model for Childhood Diseases and Vaccines, Applied Mathematical Sciences, Vol. 8, 2014, no. 98, 4859-4866.
[13] R. Garrappa, Trapezoidal methods for fractional differential equations: Theoretical and computational aspects, Mathematics and Computers in Simulation, 110 (2015), 96–112.
[14] A. A. Kilbas.; H. M. Srivastava.; and J. J. Trujillo.; Theory and Applications of Fractional Differential Equations, Elsevier Science, Amsterdam, The Netherlands,204 (2006).
[15] C. Li, C. Tao; On the fractional Adams method, Computers and Mathematics with Applications„58 (2009), 1573–1588.
[16] X. Liu, Y. Takeuchib and S. Iwami; SVIR epidemic models with vaccination strategies, Journal of Theoretical Biology, 253 (2008), 1–11.
[17] I. A. Moneim, G. A. Mosa; Modelling the hepatitis C with different types of virus genome, Computational and Mathematical Methods in Medicine, Vol. 7, No. 1, March 2006, 3-13.
[18] D. Matignon; Stability results for fractional differential equations with applications to control processing, Computational Engineering in Systems and Applications, Multi-conference, vol. 2, IMACS, IEEE-SMC Proceedings, Lille, France, 2 (1996), 963-968.
[19] I. Podlubny.; Fractional Differential Equations, Academic Press, New York, NY, USA (1999).
[20] https://en.wikipedia.org/wiki/Sofosbuvir.
Cite This Article
  • APA Style

    Moustafa El-Shahed, Ahmed. M. Ahmed, Ibrahim. M. E. Abdelstar. (2016). Fractional Calculus Model for the Hepatitis C with Different Types of Virus Genome. International Journal of Systems Science and Applied Mathematics, 1(3), 23-29. https://doi.org/10.11648/j.ijssam.20160103.12

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    ACS Style

    Moustafa El-Shahed; Ahmed. M. Ahmed; Ibrahim. M. E. Abdelstar. Fractional Calculus Model for the Hepatitis C with Different Types of Virus Genome. Int. J. Syst. Sci. Appl. Math. 2016, 1(3), 23-29. doi: 10.11648/j.ijssam.20160103.12

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    AMA Style

    Moustafa El-Shahed, Ahmed. M. Ahmed, Ibrahim. M. E. Abdelstar. Fractional Calculus Model for the Hepatitis C with Different Types of Virus Genome. Int J Syst Sci Appl Math. 2016;1(3):23-29. doi: 10.11648/j.ijssam.20160103.12

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  • @article{10.11648/j.ijssam.20160103.12,
      author = {Moustafa El-Shahed and Ahmed. M. Ahmed and Ibrahim. M. E. Abdelstar},
      title = {Fractional Calculus Model for the Hepatitis C with Different Types of Virus Genome},
      journal = {International Journal of Systems Science and Applied Mathematics},
      volume = {1},
      number = {3},
      pages = {23-29},
      doi = {10.11648/j.ijssam.20160103.12},
      url = {https://doi.org/10.11648/j.ijssam.20160103.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20160103.12},
      abstract = {In this paper, a fractional order model to study the spread of HCV-subtype 4a amongst the Egyptian population is constructed. The stability of the boundary and positive fixed points is studied. The generalized Adams-Bashforth-Moulton method is used to solve and simulate the system of fractional differential equations.},
     year = {2016}
    }
    

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    AU  - Moustafa El-Shahed
    AU  - Ahmed. M. Ahmed
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    T2  - International Journal of Systems Science and Applied Mathematics
    JF  - International Journal of Systems Science and Applied Mathematics
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    AB  - In this paper, a fractional order model to study the spread of HCV-subtype 4a amongst the Egyptian population is constructed. The stability of the boundary and positive fixed points is studied. The generalized Adams-Bashforth-Moulton method is used to solve and simulate the system of fractional differential equations.
    VL  - 1
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Author Information
  • Department of Mathematics, Faculty of Art and Sceinces, Qassim University, Qassim, Unizah, Saudi Arabia

  • Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt

  • Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt

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