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

Moustafa El-Shahed; Ahmed. M. Ahmed; Ibrahim. M. E. Abdelstar

doi:doi:10.11648/j.ijssam.20160103.12

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

Moustafa El-Shahed, Ahmed. M. Ahmed, Ibrahim. M. E. Abdelstar

Published in International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 3)

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.
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[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.
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[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.
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[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.
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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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TY  - JOUR
T1  - Fractional Calculus Model for the Hepatitis C with Different Types of Virus Genome
AU  - Moustafa El-Shahed
AU  - Ahmed. M. Ahmed
AU  - Ibrahim. M. E. Abdelstar
Y1  - 2016/10/11
PY  - 2016
N1  - https://doi.org/10.11648/j.ijssam.20160103.12
DO  - 10.11648/j.ijssam.20160103.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 23
EP  - 29
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20160103.12
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
IS  - 3
ER  -

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Author Information

Moustafa El-Shahed

Department of Mathematics, Faculty of Art and Sceinces, Qassim University, Qassim, Unizah, Saudi Arabia
Ahmed. M. Ahmed

Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt
Ibrahim. M. E. Abdelstar

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - Fractional Calculus Model for the Hepatitis C with Different Types of Virus Genome
AU  - Moustafa El-Shahed
AU  - Ahmed. M. Ahmed
AU  - Ibrahim. M. E. Abdelstar
Y1  - 2016/10/11
PY  - 2016
N1  - https://doi.org/10.11648/j.ijssam.20160103.12
DO  - 10.11648/j.ijssam.20160103.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 23
EP  - 29
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20160103.12
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
IS  - 3
ER  -

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