A fractional-order model of HIV infection with drug therapy effect

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dc.AffiliationOctober University for modern sciences and Arts (MSA)
dc.contributor.authorArafa, AAM
dc.contributor.authorRida, SZ
dc.contributor.authorKhalil, M
dc.date.accessioned2020-01-29T07:18:59Z
dc.date.available2020-01-29T07:18:59Z
dc.date.issued2014
dc.descriptionMSA Google Scholaren_US
dc.description.abstractIn this paper, the fractional-order model that describes HIV infection of CD4+ T cells with therapy effect is given. Generalized Euler Method (GEM) is employed to get numerical solution of such problem. The fractional derivatives are described in the Caputo sense.en_US
dc.identifier.citationE. Ahmed, A.M.A. El-Sayed, H.A.A. El-Saka Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models J. Math. Anal. Appl., 325 (2007), pp. 542-553 ArticleDownload PDFView Record in ScopusGoogle Scholar [2] A.A.M. Arafa, S.Z. Rida, M. Khalil Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection Nonlinear Biomed. Phys., 6 (2012), pp. 1-7 View Record in ScopusGoogle Scholar [3] A.A.M. Arafa, S.Z. Rida, M. Khalil The effect of anti-viral drug treatment of human immunodeficiency Appl. Math. Modell., 37 (2013), pp. 2189-2196 ArticleDownload PDFView Record in ScopusGoogle Scholar [4] K.S. Cole Electric conductance of biological systems Proc. Cold Spring Harbor Symp. Quant. Biol, Cold Spring Harbor, New York (1993), pp. 107-116 View Record in ScopusGoogle Scholar [5] R.V. Culshaw, S. Ruan A delay-differential equation model of HIV infection of CD4+ T -cells Math. Biosci., 165 (2000), pp. 27-39 ArticleDownload PDFView Record in ScopusGoogle Scholar [6] Y. Ding, Haiping Ye A fractional-order differential equation model of HIV infection of CD C T-cells Math. Comput. Modell., 50 (2009), pp. 386-392 ArticleDownload PDFView Record in ScopusGoogle Scholar [7] V.D. Djordjević, J. Jarić, B. Fabry, J.J. Fredberg, D. Stamenović Fractional derivatives embody essential features of cell rheological behavior Ann. Biomed. Eng., 31 (2003), pp. 692-699 View Record in ScopusGoogle Scholar [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 Int. J. Nonlinear Sci., 7 (2009), pp. 485-492 View Record in ScopusGoogle Scholar [9] A.M.A. El-Sayed, A.E.M. El-Mesiry, H.A.A. El-Saka Numerical solution for multi-term fractional (arbitrary) orders differential equations Comput. Appl. Math., 23 (2004), pp. 33-54 View Record in ScopusGoogle Scholar [10] I. Hashim, O. Abdulaziz, S. Momani Homotopy analysis method for fractional IVPs Commun. Nonlinear Sci. Numer. Simul., 14 (2009), pp. 674-684 ArticleDownload PDFView Record in ScopusGoogle Scholar [11] I.S. Jesus, J.A.T. Machado, J.B. Cunha Fractional electrical impedances in botanical elements J. Vib. Control, 14 (2008), pp. 1389-1402 CrossRefView Record in ScopusGoogle Scholar [12] I.S. Jesus, J.A.T. Machado, J.B. Cunha, Fractional order electrical impedance of fruits and vegetables, in: Proceedings of the 25th IASTED International Conference Modeling, Identification, and Control, February 6–8, 2006, Lanzarote, Canary Islands, Spain, 2006. Google Scholar [13] W. Lin Global existence theory and chaos control of fractional differential equations J. Math. Anal. Appl., 332 (2007), pp. 709-726 ArticleDownload PDFView Record in ScopusGoogle Scholar [14] M. Merdan, Tahir Khan Yev Homotopy perturbation method for solving viral dynamical model C.Ü. Fen-EdebiyatFakültesi, Fen BilimleriDergisi, 31 (2010), pp. 65-77 View Record in ScopusGoogle Scholar [15] P.W. Nelson, A.S. Perelson Mathematical analysis of delay differential equation models of HIV-1 infection Math. Biosci., 179 (2002), p. 73 ArticleDownload PDFView Record in ScopusGoogle Scholar [16] Z. Odibat, Shaher Moamni An algorithm for the numerical solution of differential equations of fractional order J. Appl. Math. Inform., 26 (2008), pp. 15-27 View Record in ScopusGoogle Scholar [17] Z. Odibat, N. Shawagfeh Generalized Taylor’s formula Appl. Math. Comput., 186 (2007), pp. 286-293 ArticleDownload PDFView Record in ScopusGoogle Scholar [18] A.S. Perelson Modeling the interaction of the immune system with HIV C. Castillo-Chavez (Ed.), Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomathematics, vol. 83, Springer, New York (1989), p. 350 CrossRefGoogle Scholar [19] A.S. Perelson, D.E. Kirschner, R. De Boer Dynamics of HIV infection of CD4+ T cells Math. Biosci., 114 (1993), pp. 81-125 ArticleDownload PDFView Record in ScopusGoogle Scholar [20] L.M. Petrovic, D.T. Spasic, T.M. Atanackovic On a mathematical model of a human root dentin Dental Mater., 21 (2005), pp. 125-128 ArticleDownload PDFView Record in ScopusGoogle Scholar [21] S.Z. Rida, H.M. El-Sherbiny, A.A.M. Arafa On the solution of the fractional nonlinear Schrödinger equation Phys. Lett. A, 372 (2008), pp. 553-558 ArticleDownload PDFView Record in ScopusGoogle Scholar [22] F.A. Rihan Numerical modeling of fractional-order biological systems Abstract Appl. Anal., 2013 (2013) Google Scholar [23] L. Rong, M.A. Gilchrist, Z. Feng, A.S. Perelson Modeling within host HIV-1 dynamics and the evolution of drug resistance: tradeoffs between viral enzyme function and drug susceptibility J. Theoret. Biol., 247 (2007), pp. 804-818 ArticleDownload PDFView Record in ScopusGoogle Scholar [24] L. Ronga, Zhilan Fenga, Alan S. Perelsonb Emergence of HIV-1 drug resistance during antiretroviral treatment Bull. Math. Biol., 69 (2007), pp. 2027-2060 Google Scholar [25] P.K. Srivastava, M. Banerjee, Peeyush Chandra Modeling the drug therapy for HIV infection J. Biol. Syst., 17 (2009), pp. 213-223 View Record in ScopusGoogle Scholar [26] H.C. Tuckwell, Frederic Y.M. Wan On the behavior of solutions in viral dynamical models Bio Systems, 73 (2004), pp. 157-161 ArticleDownload PDFView Record in ScopusGoogle Scholar [27] L. Wang, Michael Y. Li Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells Math. Biosci., 200 (2006), pp. 44-57 ArticleDownload PDFView Record in ScopusGoogle Scholaren_US
dc.identifier.doihttps://doi.org/10.1016/j.joems.2013.11.001
dc.identifier.otherhttps://doi.org/10.1016/j.joems.2013.11.001
dc.identifier.urihttps://t.ly/v8KnW
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofseriesJournal of the Egyptian Mathematical Society;Volume 22, Issue 3, October 2014, Pages 538-543
dc.subjectFractional calculusen_US
dc.subjectEuler methodlen_US
dc.subjectHIV modelen_US
dc.titleA fractional-order model of HIV infection with drug therapy effecten_US
dc.typeArticleen_US

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