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

Abstract EN

We study a fractional differential model of HIV infection of CD4 + T-cell, in which the CD4 + 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 τ ≥ 0 .

We calculate the basic reproductionnumber R 0 , the IFE E 0 , two IPEs E 1 * and E 2 * , 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.