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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 11, 2015

Dynamical analysis of the avian-human influenza epidemic model using the semi-analytical method

Azizeh Jabbari, Hossein Kheiri and Ahmet Bekir
From the journal Open Engineering

Abstract

In this work, we present a dynamic behavior of the avian-human influenza epidemic model by using efficient computational algorithm, namely the multistage differential transform method(MsDTM). The MsDTM is used here as an algorithm for approximating the solutions of the avian-human influenza epidemic model in a sequence of time intervals. In order to show the efficiency of the method, the obtained numerical results are compared with the fourth-order Runge-Kutta method (RK4M) and differential transform method(DTM) solutions. It is shown that the MsDTM has the advantage of giving an analytical form of the solution within each time interval which is not possible in purely numerical techniques like RK4M.

References

[1] Zhou J.K., Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuhan, China, 1986. Search in Google Scholar

[2] Ayaz F., Solutions of the system of differential equations by differential transform method, Appl. Math. Comput., 2004, 147, 547–567. 10.1016/S0096-3003(02)00794-4Search in Google Scholar

[3] Ayaz F., Application of differential transform method to differential-algebraic equations, Appl. Math. Comput., 2004, 152, 649–657. 10.1016/S0096-3003(03)00581-2Search in Google Scholar

[4] Odibat Z., Momani S., Generalized differential transform method for linear partial differential equations of fractional order, Appl. Math. Lett., 2008, 21, 194–199. 10.1016/j.aml.2007.02.022Search in Google Scholar

[5] Momani S., Odibat Z., A novel method for nonlinear fractional partial differential equations: combination of DTM and generalized Taylor’s formula, J.Comput. Appl.Math., 2008, 220, 85–95. 10.1016/j.cam.2007.07.033Search in Google Scholar

[6] Odibat Z., Momani S., Erturk V., Generalized differential transform method: application to differential equations of fractional order, Appl. Math. Comput., 2008, 197, 467–477. 10.1016/j.amc.2007.07.068Search in Google Scholar

[7] Kuo B., Lo C., Application of the differential transformation method to the solution of a damped system with high nonlinearity, Nonlinear Anal., 2009, 70, 1732–1737. 10.1016/j.na.2008.02.056Search in Google Scholar

[8] Al-Sawalha M., Noorani M., Application of the differential transformation method for the solution of the hyperchaotic Rössler system, Commun. Nonlinear Sci. Numer. Simul., 2009, 14, 1509–1514. 10.1016/j.cnsns.2008.02.002Search in Google Scholar

[9] Gokdogan A., Yildirim A., Merdan M., Solving a fractional order model of HIV infection of CD4+ T cells, Math. Comput. Model., 2011, 54, 2132–2138. 10.1016/j.mcm.2011.05.022Search in Google Scholar

[10] Gokdogan A., Merdan M., Yildirim A., A multistage differential transformation method for approximate solution of Hantavirus infection model, Commun. Nonlinear Sci. Numer. Simul., 2012, 17, 1–8. 10.1016/j.cnsns.2011.05.023Search in Google Scholar

[11] Gokdogan A., Merdan M., Yildirim A., Adaptive multi-step differential transformation method to solving nonlinear differential equations, Math. Comput. Model., 2012, 55, 761–769. 10.1016/j.mcm.2011.09.001Search in Google Scholar

[12] Iwami S., Takeuchi Y., Liu X., Avian-human influenza epidemic model, Math. Bio., 2007, 207, 1–25. 10.1016/j.mbs.2006.08.001Search in Google Scholar

[13] Pukhov G.E., Differential Transformations of functions and equations, Naukova Dumka, Kiev, 1980 (in Russian). Search in Google Scholar

[14] Chen C.L., Lin S.H., Chen C.K., Application of Taylor transformation to nonlinear predictive control problem, Appl. Math. Modell., 1996, 20, 699–710. 10.1016/0307-904X(96)00050-9Search in Google Scholar

[15] Yeh Y.L., Wang C.C., Jang M.J., Using finite difference and differential transformation method to analyze of large deflections of orthotropic rectangular plate problem, Appl. Math. Comp., 2007, 190, 1146–1156. 10.1016/j.amc.2007.01.099Search in Google Scholar

[16] Abdel-Halim Hassan I.H., Application to differential transformation method for solving systems of differential equations, Appl. Math. Modell., 2008, 32, 2552–2559. 10.1016/j.apm.2007.09.025Search in Google Scholar

[17] Jang M.J., Chen C.L., Analysis of the response of a strongly nonlinear damped system using a differential transformation technique, Appl. Math. Comput., 1997, 88, 137–151. 10.1016/S0096-3003(96)00308-6Search in Google Scholar

[18] Hwang I., Li J., Du D., A numerical algorithm for optimal control of a class of hybrid systems: Differential transformation based approach, Internat. J. Control., 2008, 81, 277–293. 10.1080/00207170701556880Search in Google Scholar

Received: 2014-8-3
Accepted: 2015-2-9
Published Online: 2015-3-11

©2015 A. Jabbari et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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