Applied and Computational Mathematics
Volume 4, Issue 2, April 2015, Pages: 77-82
Received: Mar. 9, 2015;
Accepted: Mar. 24, 2015;
Published: Mar. 30, 2015
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Bonyah Ebenezer, Department of Mathematics and Statistics, Kumasi Polytechnic, Kumasi, Ghana
This paper examines the fractional order of influenza using an epidemic model. The stability of disease-free and positive fixed points is explored and studied. The Adams-Bashforth-Moulton algorithm is employed to determine the solution and also simulate the system of differential equations. It is observed that Adams-Bashforth-Moulton method gives similar results as obtained in Runge-Kutta technique and ODE 45.
On Fractional Order Influenza A Epidemic Model, Applied and Computational Mathematics.
Vol. 4, No. 2,
2015, pp. 77-82.
Matignon D. 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.
E. Ahmed E, El-Sayed A. M. A., El-Mesiry E. M., El-Saka. H. A. A.(2005).Numerical solution for the fractional replicator equation, IJMPC,(2005) 16, 1–9.
Ahmed E., El-Sayed A. M. A., El-Saka H. A. A. 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.
Ahmed E., El-Sayed A. M. A., El-Saka. H. A. A. Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models, J. Math. Anal. Appl, 325 (2007), 542–553.
Liu X., Takeuchib Y., Iwami S. SVIR epidemic models with vaccination strategies, Journal of Theoretical Biology, 253 (2008), 1–11.
Elbasha E. H., Gumel. A. B. Analyzing the dynamics of an SIRS vaccination model with waning natural and vaccine-induced immunity, Trends in Parasitology, 12 (2011) ,2692–2705.
Li and C., Tao C. On the fractional Adams method,” Computers and Mathematics with Applications, vol. 58, no. 8,(2009) pp. 1573–1588.
Diethelm K. An algorithm for the numerical solution of differential equations of fractional order,” Electronic Transactions on Numerical Analysis, vol. 5,(1997) pp. 1–6.
Diethelm K., Ford N. J. Analysis of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 265, no. 2,(2002) pp. 229–248.
R. Anderson and R. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991
S. B. Thacker, The persistence of influenza in human populations, Epidemiol. Rev., 8, (1986),129–142.
H. W. Hethcote, Qualitative analyses of communicable disease models, Math. Biosci., 28, (1976),335–356.
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42(4),(2000), 599–653.
M. Nu˜no, Z. Feng, M. Martcheva, C. C. Chavez, Dynamics of two-strain influenza with isolation and cross-protection, SIAM J. Appl. Math., 65, 3,(2005), 964–982.
Kilbas A.A., Srivastava H. M., Trujillo J. J. (2006) Theory and Application Fractional Differential Equations, Elseviesr, Amsterdam, The Netherlands,(2006).
M. El hia , O. Balatif , J. Bouyaghroumni, E. Labriji, M. Rachik. Optimal control applied to the spread of Inuenza A(H1N1). Applied Mathematical Sciences, Vol. 6, 2012, no. 82,(2007), 4057 – 4065.
K. Hattaf. K and N. Yousfi. Mathematical Model of the Influenza A(HIN1) Infection. Advanced Studies in Biology, Vol.1,no.8,(2009),383-390.