THE EFFECT OF VACCINATION ON THE DYNAMICS OF CHILDHOOD DISEASES DESCRIBED BY A FRACTIONAL SIR EPIDEMIC MODEL

dc.AffiliationOctober University for modern sciences and Arts (MSA)
dc.contributor.authorRIDA, S. Z.
dc.contributor.authorABD EL RADI, A. S.
dc.contributor.authorARAFA, A.A.M.
dc.contributor.authorKHALIL, M.
dc.date.accessioned2020-02-01T10:57:15Z
dc.date.available2020-02-01T10:57:15Z
dc.date.issued2013
dc.descriptionMSA Google Scholaren_US
dc.description.abstractChildhood 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.en_US
dc.identifier.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.en_US
dc.identifier.issn2090-5858.
dc.identifier.urihttps://t.ly/8J76N
dc.language.isoenen_US
dc.publisherInternational Journal Of Advanced in Science and Technologyen_US
dc.relation.ispartofseriesJournal of Fractional Calculus and Applications;Vol. 4, No. 8, pp. 1-14.
dc.subjectChildhood diseasesen_US
dc.subjectFractional order differential equationsen_US
dc.subjectGeneralized Euler methoden_US
dc.titleTHE EFFECT OF VACCINATION ON THE DYNAMICS OF CHILDHOOD DISEASES DESCRIBED BY A FRACTIONAL SIR EPIDEMIC MODELen_US
dc.typeArticleen_US

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