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.
| Published in | Applied and Computational Mathematics (Volume 4, Issue 2) |
| DOI | 10.11648/j.acm.20150402.17 |
| Page(s) | 77-82 |
| 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. |
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Copyright © The Author(s), 2015. Published by Science Publishing Group |
Fractional Order Calculus, Influenza A, Adams-Bashforth- Moulton
| [1] | 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. |
| [2] | 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. |
| [3] | 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. |
| [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. |
| [5] | Liu X., Takeuchib Y., Iwami S. SVIR epidemic models with vaccination strategies, Journal of Theoretical Biology, 253 (2008), 1–11. |
| [6] | 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. |
| [7] | Li and C., Tao C. On the fractional Adams method,” Computers and Mathematics with Applications, vol. 58, no. 8,(2009) pp. 1573–1588. |
| [8] | 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. |
| [9] | Diethelm K., Ford N. J. Analysis of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 265, no. 2,(2002) pp. 229–248. |
| [10] | R. Anderson and R. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991 |
| [11] | S. B. Thacker, The persistence of influenza in human populations, Epidemiol. Rev., 8, (1986),129–142. |
| [12] | H. W. Hethcote, Qualitative analyses of communicable disease models, Math. Biosci., 28, (1976),335–356. |
| [13] | H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42(4),(2000), 599–653. |
| [14] | 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. |
| [15] | Kilbas A.A., Srivastava H. M., Trujillo J. J. (2006) Theory and Application Fractional Differential Equations, Elseviesr, Amsterdam, The Netherlands,(2006). |
| [16] | 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. |
| [17] | 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. |
APA Style
Bonyah Ebenezer. (2015). On Fractional Order Influenza A Epidemic Model. Applied and Computational Mathematics, 4(2), 77-82. https://doi.org/10.11648/j.acm.20150402.17
ACS Style
Bonyah Ebenezer. On Fractional Order Influenza A Epidemic Model. Appl. Comput. Math. 2015, 4(2), 77-82. doi: 10.11648/j.acm.20150402.17
AMA Style
Bonyah Ebenezer. On Fractional Order Influenza A Epidemic Model. Appl Comput Math. 2015;4(2):77-82. doi: 10.11648/j.acm.20150402.17
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Download@article{10.11648/j.acm.20150402.17,
author = {Bonyah Ebenezer},
title = {On Fractional Order Influenza A Epidemic Model},
journal = {Applied and Computational Mathematics},
volume = {4},
number = {2},
pages = {77-82},
doi = {10.11648/j.acm.20150402.17},
url = {https://doi.org/10.11648/j.acm.20150402.17},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150402.17},
abstract = {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.},
year = {2015}
}
TY - JOUR T1 - On Fractional Order Influenza A Epidemic Model AU - Bonyah Ebenezer Y1 - 2015/03/30 PY - 2015 N1 - https://doi.org/10.11648/j.acm.20150402.17 DO - 10.11648/j.acm.20150402.17 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 77 EP - 82 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20150402.17 AB - 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. VL - 4 IS - 2 ER -
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