A fractional-order model of HIV infection: Numerical solution and comparisons with data of patients

Simple item page
dc.AffiliationOctober University for modern sciences and Arts (MSA)
dc.contributor.authorArafa A.A.M.
dc.contributor.authorRida S.Z.
dc.contributor.authorKhalil M.
dc.contributor.otherDepartment of Mathematics and Computer Science
dc.contributor.otherFaculty of Sciences
dc.contributor.otherPort Said University
dc.contributor.otherPort Said
dc.contributor.otherEgypt; Department of Mathematics
dc.contributor.otherFaculty of Sciences
dc.contributor.otherSouth Valley University
dc.contributor.otherQena
dc.contributor.otherEgypt; Department of Mathematics
dc.contributor.otherFaculty of Engineering
dc.contributor.otherOctober University for Modern Sciences and Arts
dc.contributor.other6th Oct. City
dc.contributor.otherGiza
dc.contributor.otherEgypt
dc.date.accessioned2020-01-09T20:42:18Z
dc.date.available2020-01-09T20:42:18Z
dc.date.issued2014
dc.descriptionScopus
dc.descriptionMSA Google Scholar
dc.description.abstractIn this paper, a fractional-order model which describes the human immunodeficiency type-1 virus (HIV-1) infection is presented. Numerical solutions are obtained using a generalized Euler method (GEM) to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These comparisons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model. � 2014 World Scientific Publishing Company.en_US
dc.description.urihttps://www.scimagojr.com/journalsearch.php?q=21100198432&tip=sid&clean=0
dc.identifier.doihttps://doi.org/10.1142/S1793524514500363
dc.identifier.issn17935245
dc.identifier.otherhttps://doi.org/10.1142/S1793524514500363
dc.identifier.urihttps://www.worldscientific.com/doi/abs/10.1142/S1793524514500363
dc.language.isoEnglishen_US
dc.publisherWorld Scientific Publishing Co. Pte Ltden_US
dc.relation.ispartofseriesInternational Journal of Biomathematics
dc.relation.ispartofseries7
dc.subjectEuler methoden_US
dc.subjectFractional calculusen_US
dc.subjectHIV modelen_US
dc.subjectnumerical resultsen_US
dc.titleA fractional-order model of HIV infection: Numerical solution and comparisons with data of patientsen_US
dc.typeArticleen_US
dcterms.isReferencedByAini Abdullah, F., Md. Ismail, A.I., Simulations of the spread of the Hantavirus using fractional differential equations (2011) Matematika, 27, pp. 149-158; Ahmed, E., Elgazzar, A.S., On fractional-order differential equations model for nonlocal epidemics (2007) Physica A, 379, pp. 607-614; Ahmed, E., El-Saka, H.A., On fractional-order models for Hepatitis C (2010) Nonlinear Biomed. Phys., 4, p. 1; Arafa, A.A.M., Rida, S.Z., Khalil, M., Fractional order model of human T-cell lymphotropic virus i (HTLV-I) infection of CD4+T-cells (2011) Adv. Stud. Biol., 3, pp. 347-353; Arafa, A.A.M., Rida, S.Z., Khalil, M., Fractional modeling dynamics of HIV and CD4+T-cells during primary infection (2012) Nonlinear Biomed. Phys., 6, pp. 1-7; Arafa, A.A.M., Rida, S.Z., Khalil, M., The effect of anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) described by a fractional-order model (2013) Appl. Math. Model., 37, pp. 2189-2219; Ciupe, M.S., Bivort, B.L., Bortz, D.M., Nelson, P.W., Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models (2006) Math. Biosci., 200, pp. 1-27; Dalir, M., Bashour, M., Applications of fractional calculus (2010) Appl. Math. Sci., 4, pp. 1021-1032; Demirci, E., Unal, A., Ozalp, N., A fractional-order SEIR model with densitydependent death rate (2011) Hacet. J. Math. Stat., 40 (2), pp. 287-295; Deng, W., Smoothness and stability of the solutions for nonlinear fractional differential equations (2010) Nonlinear Anal., 72, pp. 1768-1777; Ding, Y., Yea, H., A fractional-order differential equation model of HIV infection of CD4+T-cells (2009) Math. Comput. Model., 50, pp. 386-392; El-Misiery, A.E.M., Ahmed, E., On a fractional model for earthquakes (2006) Appl. Comput. Math., 178, pp. 207-211; El-Sayed, A.M.A., El-Mesiry, A.E.M., El-Saka, H.A.A., Numerical solution for multi-term fractional (arbitrary) orders differential equations (2004) Comput. Appl. Math., 23, pp. 33-54; El-Sayed, A.M.A., Rida, S.Z., Arafa, A.A.M., On the solutions of time-fractional bacterial chemotaxis in a diffusion gradient chamber (2009) Int. J. Nonlinear Sci., 7, pp. 485-492; Li, C.P., Zhang, F.R., A survey on the stability of fractional differential equations (2011) European Phys. J. Spec. Top., 193, pp. 27-47; Lin, W., Global existence theory and chaos control of fractional differential equations (2007) J. Math. Anal. Appl., 332, pp. 709-726; Nelson, P.W., Perelson, A.S., Mathematical analysis of delay differential equation models of HIV-1 infection (2002) Math. Biosci., 179, p. 73; Odibat, Z., Momani, S., An algorithm for the numerical solution of differential equations of fractional order (2008) J. Appl. Math. Inform., 26, pp. 15-27; Odibat, Z., Shawagfeh, N., Generalized Taylor's formula (2007) Appl. Math. Comput., 186, pp. 286-293; Pawelek, K.A., Liu, S., Pahlevani, F., Rong, L., A model of HIV-1 infection with two time delays: Mathematical analysis and comparison with patient data (2012) Math. Biosci., 235, pp. 98-109; Perelson, A.S., Modeling the interaction of the immune system with HIV (1989) Mathematical and Statistical Approaches to AIDS Epidemiology, 83, pp. 350-370. , ed. C. Castillo-Chavez, Lecture Notes in Biomathematics Springer, New York; Perelson, A.S., Essunger, P., Ho, D.D., Dynamics of HIV-1 and CD4+ lymphocytes in vivo (1997) AIDS, 11, pp. 17-24; Perelson, A.S., Neumann, A.U., Markowitz, M., Leonard, J.M., Ho, D.D., HIV-1 dynamics in vivo: Virion clearance rate infected cell life-span, and viral generation time (1996) Science, 271, pp. 1582-1586; Petrovic, L.M., Spasic, D.T., Atanackovic, T.M., On a mathematical model of a human root dentin (2005) Dent. Mater., 21, pp. 125-128; Rong, L., Feng, Z., Perelson, A.S., Emergence of HIV-1 drug resistance during antiretroviral treatment (2007) Bull. Math. Biol., 69, pp. 2027-2060; Srivastava, P.K., Banerjee, M., Chandra, P., Modeling the drug therapy for HIV infection (2009) J. Biol. Syst., 17, pp. 213-223; Srivastava, P.K., Chandra, P., Modeling the dynamics of HIV and CD4+T-cells during primary infection (2010) Nonlinear Anal. Real World Appl., 11, pp. 612-618; Stafford, M.A., Corey, L., Cao, Y., Daar, E.S., Ho, D.D., Perelson, A.S., Modeling plasma virus concentration during primary HIV infection (2000) J. Theor. Biol., 203, pp. 285-301; Suat Ertrk, V., Odibat, Z.M., Momani, S., An approximate solution of a fractionalorder differential equation model of human T-cell lymphotropic virus i (HTLV-I) infection of CD4+T-cells (2011) Comput. Math. Appl., 62, pp. 996-1002; http://www.who.int/hiv/data/en/index.html, World Health Organization, HIV; (2012), http://www.who.int/gho/publications/worldhealthstatistics/2012/en/
dcterms.sourceScopus

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
avatar_scholar_128.png
Size:
2.73 KB
Format:
Portable Network Graphics
Description:
Download

Collections

Faculty Of Engineering Research Paper