Fractional Calculus Model for the Hepatitis C with Different Types of Virus Genome
International Journal of Systems Science and Applied Mathematics
Volume 1, Issue 3, September 2016, Pages: 23-29
Received: Sep. 6, 2016;
Accepted: Sep. 18, 2016;
Published: Oct. 11, 2016
Views 3706 Downloads 140
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; Quantitative methods Unit, Faculty of Business & Economice, Qassim University, Almulyda, Saudi Arabia
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.
Ahmed. M. Ahmed,
Ibrahim. M. E. Abdelstar,
Fractional Calculus Model for the Hepatitis C with Different Types of Virus Genome, International Journal of Systems Science and Applied Mathematics.
Vol. 1, No. 3,
2016, pp. 23-29.
E. Ahmed, A. M. A. El-Sayed, E. M. El-Mesiry and H. A. A. El-Saka; Numerical solution for the fractional replicator equation, IJMPC, 16 (2005), 1–9.
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.
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.
R. M. Anderson; R. M. May; Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991.
L. Debnath; Recent applications of fractional calculus to science and engineering. International Journal of Mathematics and Mathematical Sciences, 54 (2003) 3413–3442.
K. Diethelm, N. J. Ford; Analysis of fractional differential equations, J Math Anal Appl, 256 (2002), 229–248.
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.
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.
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.
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.
M. Elshahed and A. Alsaedi; The Fractional SIRC Model and Influenza A, Mathematical Problems in Engineering, Article ID 480378 (2011), 1–9.
M. Elshahed, F. Abd El-Naby; Fractional Calculus Model for Childhood Diseases and Vaccines, Applied Mathematical Sciences, Vol. 8, 2014, no. 98, 4859-4866.
R. Garrappa, Trapezoidal methods for fractional differential equations: Theoretical and computational aspects, Mathematics and Computers in Simulation, 110 (2015), 96–112.
A. A. Kilbas.; H. M. Srivastava.; and J. J. Trujillo.; Theory and Applications of Fractional Differential Equations, Elsevier Science, Amsterdam, The Netherlands,204 (2006).
C. Li, C. Tao; On the fractional Adams method, Computers and Mathematics with Applications„58 (2009), 1573–1588.
X. Liu, Y. Takeuchib and S. Iwami; SVIR epidemic models with vaccination strategies, Journal of Theoretical Biology, 253 (2008), 1–11.
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.
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.
I. Podlubny.; Fractional Differential Equations, Academic Press, New York, NY, USA (1999).