THE EFFECT OF VACCINATION ON THE DYNAMICS OF CHILDHOOD DISEASES DESCRIBED BY A FRACTIONAL SIR EPIDEMIC MODEL
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Date
2013
Journal Title
Journal ISSN
Volume Title
Type
Article
Publisher
International Journal Of Advanced in Science and Technology
Series Info
Journal of Fractional Calculus and Applications;Vol. 4, No. 8, pp. 1-14.
Doi
Scientific Journal Rankings
Abstract
Childhood vaccination programs have had a dramatic impact on
reducing child mortality worldwide. We introduce fractional-order into A SIR
model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is presented in this paper. Generalized Euler method
(GEM) is considered in this paper to obtain an analytic approximate solution
of this model. The obtained results proved that the disease will persist within
the population if the vaccination coverage level is below a certain threshold.
Description
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Keywords
Childhood diseases, Fractional order differential equations, Generalized Euler method
Citation
[1] A. Yildirim, Y. Cherruault, Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method, emerald, 38(2009) 1566- 1575. [2] A.A.M. Arafa, S.Z. Rida and M. Khalil, Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection, Nonlinear Biomedical Physics 6( 2012) 1-7. [3] A.A.M. Arafa, S.Z. Rida and M. Khalil, Fractional Order Model of Human T-cell Lymphotropic Virus I (HTLV-I) Infection of CD4+T-cells, Advanced Studies in Biology, 3(2011) 347 - 353. [4] J. Biazar, Solution of the epidemic model by Adomian decomposition method, App. Math. comput., 173 (2) (2006) 1101-1106. [5] S. Busenberg, P. van den Driessche, Analysis of a disease transmission model in a population with varying size, J. Math. Biol. 28 (1990) 257-270. [6] K.S. Cole, Electric conductance of biological systems, in: Proc. Cold Spring Harbor Symp. Quant. Biol, Cold Spring Harbor, New York, (1993) 107-116. [7] K. Diethelm and G. Walz, Numerical solution for fractional differential equations by extrapolation, Numerical algoritms ,16 (1997) 231-253.[8] A.M.A. El-Sayed, S.Z. Rida, A.A.M. Arafa, On the Solutions of Time-fractional Bacterial Chemotaxis in a Diffusion Gradient Chamber, International Journal of Nonlinear Science , 7(2009) 485-492. [9] A.M.A. El-Sayed, S.Z. Rida, A.A.M. Arafa, Exact Solutions of Fractional-Order Biological Population Model, Commun. Theor. Phys. 52 (2009) 992-996. [10] A.M.A. El-Sayed, A. E. M. El-Mesiry, and H. A. A. El-Saka, Numerical solution for multi-term fractional (arbitrary) orders differential equations, Comput. Appl. Math., 23(2004)33-54. [11] I. Hashim, O. Abdulaziz, S. Momani, Homotopy analysis method for fractional IVPs, Communications in Nonlinear Science and Numerical Simulation 14 (2009) 674-684. [12] O.D. Makinde, Adomian decomposition approach to a SIR epidemic model with constant vaccination strategy, App. Math. comput., 184 (2007) 842-848. [13] M. Merdan, Homotopy perturbation method for solving a model for HIV infection of CD4+ T cells, Istanbul Ticaret Universitesi Fen Bilimleri Dergisi, 6 (2007) 59-62. [14] S.Z. Rida, H.M. El-Sherbiny, A.A.M. Arafa, On the solution of the fractional nonlinear Schrodinger equation, Physics Letters A, 372 (2008) 553-558. [15] H.L. Smith, Subharmonic bifurcation in SIR epidemic model, J. Math. Biol. 17 (1983) 163- 177. [16] Z. M. Odibat, and Shaher Moamni, An algorithm for the numerical solution of differential equations of fractional order, J. Appl. Math. & Informatics, 26(2008) 15 - 27. [17] Z. Odibat and N. Shawagfeh, Generalized Taylor’s formula, Appl. Math. Comput. 186 (2007) 286-293.