We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

A New Modification of the Differential Transform Method for a SIRC Influenza Model

by S. F. M. Ibrahim, S. M. Ismail
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 69 - Number 19
Year of Publication: 2013
Authors: S. F. M. Ibrahim, S. M. Ismail
10.5120/12077-8020

S. F. M. Ibrahim, S. M. Ismail . A New Modification of the Differential Transform Method for a SIRC Influenza Model. International Journal of Computer Applications. 69, 19 ( May 2013), 8-15. DOI=10.5120/12077-8020

@article{ 10.5120/12077-8020,
author = { S. F. M. Ibrahim, S. M. Ismail },
title = { A New Modification of the Differential Transform Method for a SIRC Influenza Model },
journal = { International Journal of Computer Applications },
issue_date = { May 2013 },
volume = { 69 },
number = { 19 },
month = { May },
year = { 2013 },
issn = { 0975-8887 },
pages = { 8-15 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume69/number19/12077-8020/ },
doi = { 10.5120/12077-8020 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:30:40.114380+05:30
%A S. F. M. Ibrahim
%A S. M. Ismail
%T A New Modification of the Differential Transform Method for a SIRC Influenza Model
%J International Journal of Computer Applications
%@ 0975-8887
%V 69
%N 19
%P 8-15
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, approximate analytical solution of SIRC model associated with the evolution of influenza A disease in human population is acquired by the modified differential transform method (MDTM). The differential transform method (DTM) is mentioned in summary. MDTM can be obtained from DTM applied to Laplace, inverse Laplace transform and padé approximant. The MDTM is used to increase the accuracy and accelerate the convergence rate of truncated series solution getting by the DTM. The analytical-numerical technique can be used in order to produce simulations with different initial conditions, parameter values for different values of the basic reproduction number.

References
  1. Palese, P. and Young, J. 1982. Variation of influenza A, B, and C viruses. (Science 215)1468-1474.
  2. Casagrandi, R. , Bolzoni, L. , Levin, S. A. , and Andreasen, V. 2006. The SIRC model and influenza A, Math. Biosci. (200) 152-169.
  3. Kermack, W. O. and McKendrick, A. G. 1927. Contributions to the mathematical theory of epidemics, Part I, Proc. Roy. Sot. Ser. , A 115 , 700-721.
  4. Samanta, G. P. 2010. Global Dynamics of a Nonautonomous SIRC Model for Influenza A with Distributed Time Delay, Differ Equ Dyn Syst, 18 341-362.
  5. Jodar, L. , Villanueva, R. J. , Arenas, A. J. , and Gonz´alez, G. C. 2008. Nonstandard numerical methods for a mathematical model for influenza disease, Mathematics and Computers in Simulation (79 ) 622-633.
  6. Zhou, J. K. 1986. Differential Transform and its Applications for Electrical Circuits,Wuhan, Huarjung University Press.
  7. Baker, G. A. 1975. Essentials of padé approximants. London: Academic press; .
  8. Chang, S. H. , and Chang, I. L. 2008 A new algorithm for calculating one-dimensional differential transform of nonlinear functions. Appl Math Comput ;195:799-808.
  9. Jordan, D. W. , and Smith, P. 1999. Nonlinear Ordinary Differential Equations. Oxford University Press.
  10. Dehghan, M. , Shakourifar, M. , and Hamidi, A. 2009. The solution of linear and nonlinear systems of Volterra functional equations using Adomian. Padé technique. Chaos Solitons Fract ;39:2509-21.
  11. Dehghan, M. , Hamidi, A. , and Shakourifar, M. 2007. The solution of coupled Burgers equations using Adomian. Padé technique. Appl Math Comput ; 189:1034-47.
  12. Chinviriyasit, W. 2007. Numerical modeling of the transmission dynamics of influenza, The First Inter. Symp. on Optim. and Sys. Biol. , pp. 52-59.
  13. Pukhov, G. E. 1980. Differential transformations of functions and equations. Naukova Dumka, Kiev, (in Russian).
  14. Chen, S. S. and Chen, C. K. 2009 Application of the differential transformation method to the free vibrations of strongly non-linear oscillators, Nonlinear Analysis: Real World Applications 10 881-888.
  15. Yen-Liang Yeh, Cheng Chi Wang, Ming-Jyi Jang, 2007. Using finite difference and differential transformation method to analyze of large deflections of orthotropic rectangular plate problem. Appl. Math. Comput. ; 190(2) 1146-1156.
  16. Abdel-Hialim Hassan, I. H. 2008 Application to differential transformation method for solving systems of differential equations Appl. Math Modelling ; 32(12)2552-2559.
  17. Jang, M. J. and Chen, C. L. 1997. Analysis of the response of astrongly nonlinear damped system using a differential transformation technique. Appl. Math Comput. ; 88(2-3): 137-151.
  18. Chen Chao-Kuang, Ho Shing-Huei. 1996. Application of differential transformation to eigenvalue problems. Appl Math Comput ; 79: 173-88.
Index Terms

Computer Science
Information Sciences

Keywords

SIRC model Epidemic models Modified Differential transformation method padé approximants

Powered by PhDFocusTM