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

摘要

We study a fractional differential model of HIV infection ofCD4+T-cell, in which theCD4+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 forτ≥0. We calculate the basic reproductionnumberR0, the IFEE0, two IPEsE1*andE2*, 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.