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

Abstract

We study a fractional differential model of HIV infection of ${\text{CD4}}^{\text{+}}$ T-cell, in which the ${\text{CD4}}^{\text{+}}$ 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 $\tau \ge 0$. We calculate the basic reproduction number $R_0$, 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.