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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 291614, 13 pages
http://dx.doi.org/10.1155/2014/291614
Research Article

Numerical Analysis for a Fractional Differential Time-Delay Model of HIV Infection of CD4+ T-Cell Proliferation under Antiretroviral Therapy

1College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, China
2Departamento de Matematica, Universidad Tecnica Federico Santa Maria, Casilla 110-V, Valparaiso, Chile

Received 2 October 2013; Accepted 11 December 2013; Published 12 February 2014

Academic Editor: Abdon Atangana

Copyright © 2014 Yiliang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a fractional differential model of HIV infection of T-cell, in which the T-cell proliferation plays an important role in HIV infection under antiretroviral therapy. An appropriate method is given to ensure that both the equilibria are asymptotically stable for . We calculate the basic reproduction number , the IFE , two IPEs and , and so on, and judge the stability of the equilibrium. In addition, we describe the dynamic behaviors of the fractional HIV model by using the Adams-type predictor-corrector method algorithm. At last, we extend the model to incorporate the term which we consider the loss of virion and a bilinear term during attacking the target cells.