On fractional order dengue epidemic model

Mathematical Problems in Engineering

Volumn 2014, Issue , 2014, Pages

  Al Sulami, Hamed ^a   El Shahed, Moustafa ^a,b   Nieto, Juan J ^a,c   Shammakh, Wafa ^a  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b QASSIM UNIVERSITY   (Saudi Arabia)

^c UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EPIDEMIC MODELING; FRACTIONAL ORDER;

EID: 84907228613     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2014/456537     Document Type: Article

References (23)

1. Rodrigues H. S., Monteiro M. T., Torres D. F. M., Sensitivity analysis in a dengue epidemiological model. Conference Papers in Mathematics 2013 2013 7 721406 10.1155/2013/721406
2. WHO, Dengue: Guidelines for Diagnosis, Treatment, Prevention and Control 2009 2nd Geneva, Switzerland World Health Organization
3. Esteva L., Vargas C., Analysis of a dengue disease transmission model. Mathematical Biosciences 1998 150 2 131 151 10.1016/S0025-5564(98)10003-2 2-s2.0-0032526469 ZBL0930.92020
4. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Application Fractional Differential Equations 2006 Amsterdam, The Netherlands Elseviesr
5. Podlubny I., Fractional Differential Equations 1999 New York, NY, USA Academic Press ZBL1225.34011
6. Pooseh S., Rodrigues H. S., Torres D. F. M., Fractional derivatives in dengue epidemics. Proceedings of the International Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics (ICNAAM '11) September 2011 739 742 10.1063/1.3636838 ZBL1225.34011 2-s2.0-81855167707
7. Anderson R., May R., Infectious Disease of Humans, Dynamics and Control 1995 Oxford, UK Oxford University Press ZBL1142.30303
8. Elbasha E. H., Podder C. N., Gumel A. B., Analyzing the dynamics of an SIRS vaccination model with waning natural and vaccine-induced immunity. Nonlinear Analysis: Real World Applications 2011 12 5 2692 2705 10.1016/j.nonrwa.2011.03.015 2-s2.0-79957897316 ZBL1225.37104
9. Hethcote H., Zhien M., Shengbing L., Effects of quarantine in six endemic models for infectious diseases. Mathematical Biosciences 2002 180 141 160 10.1016/S0025-5564(02)00111-6 2-s2.0-0036846383 ZBL1019.92030
10. Gorenflo R., Loutschko J., Luchko Y., Computation of the Mittag-Lefflerfunction E β (z) and its derivatives. Fractional Calculus and Applied Analysis 2002 5 491 518
11. Ahmed E., El-Sayed A. M. A., El-Mesiry A. E. M., El-Saka H. A. A., Numerical solution for the fractional replicator equation. International Journal of Modern Physics C 2005 16 7 1017 1025 10.1142/S0129183105007698 2-s2.0-30444447948 ZBL1080.65536
12. 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, Rössler, Chua and Chen systems. Physics Letters A: General, Atomic and Solid State Physics 2006 358 1 1 4 10.1016/j.physleta.2006.04.087 2-s2.0-33746648126 ZBL1142.30303
13. 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. Journal of Mathematical Analysis and Applications 2007 325 1 542 553 10.1016/j.jmaa.2006.01.087 2-s2.0-33750295344 ZBL1142.30303
14. Matignon D., Stability results for fractional differential equations with applications to control processing. 2 Proceedings of the Computational Engineering in Systems Applications 1996 Lille, France 963 968
15. Diethelm K., An algorithm for the numerical solution of differential equations of fractional order. Electronic Transactions on Numerical Analysis 1997 5 1 6 ZBL0890.65071 2-s2.0-0001618393
16. Diethelm K., Ford N. J., Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications 2002 265 2 229 248 10.1006/jmaa.2000.7194 2-s2.0-0037081673 ZBL1014.34003
17. Ding Y., Ye H., A fractional-order differential equation model of HIV infection of CD4+ T-cells. Mathematical and Computer Modelling 2009 50 3-4 386 392 2-s2.0-67549148317 10.1016/j.mcm.2009.04.019 ZBL1185.34005
18. Ye H., Ding Y., Nonlinear dynamics and chaos in a fractional-order HIV model. Mathematical Problems in Engineering 2009 2009 12 378614 10.1155/2009/378614 ZBL1181.37124 2-s2.0-67651225426
19. Li C., Tao C., On the fractional Adams method. Computers and Mathematics with Applications 2009 58 8 1573 1588 10.1016/j.camwa.2009.07.050 2-s2.0-69749102394 ZBL1189.65142
20. Diethelm K., Ford N. J., Freed A. D., A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics 2002 29 1-4 3 22 10.1023/A:1016592219341 2-s2.0-0036650479 ZBL1009.65049
21. Soewono E., Supriatna A. K., A Two-dimensional model for transmission of dengue fever disease. Bulletin of the Malaysian Mathematical Sciences Society 2001 24 48 57 ZBL0998.92036
22. Demirci E., Unal A., Özalp N., A fractional order SEIR model with density dependent death rate. Hacettepe Journal of Mathematics and Statistics 2011 40 2 287 295 2-s2.0-80052720875 ZBL1262.92032
23. Özalp N., Demiörciö E., A fractional order SEIR model with vertical transmission. Mathematical and Computer Modelling 2011 54 1-2 1 6 2-s2.0-79955465694 10.1016/j.mcm.2010.12.051 ZBL1225.34011