Arafa A.A.M.Rida S.Z.Khalil M.Department of Mathematics and Computer ScienceFaculty of SciencesPort Said UniversityPort SaidEgypt; Department of MathematicsFaculty of SciencesSouth Valley UniversityQenaEgypt; Department of MathematicsFaculty of EngineeringOctober University for Modern Sciences and Arts6th Oct. CityGizaEgypt2020-01-092020-01-09201417935245https://doi.org/10.1142/S1793524514500363https://www.worldscientific.com/doi/abs/10.1142/S1793524514500363ScopusMSA Google ScholarIn 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.EnglishEuler methodFractional calculusHIV modelnumerical resultsArticlehttps://doi.org/10.1142/S1793524514500363