In this paper, we study the HIV infection model based on fractional derivative with
particular focus on the degree of T-cell depletion that can be caused by viral
cytopathicity. The arbitrary order of the fractional derivatives gives an additional
degree of freedom to fit more realistic levels of CD4+ cell depletion seen in many AIDS
patients. We propose an implicit numerical scheme for the fractional-order HIV model
using a finite difference approximation of the Caputo derivative. The fractional system
has two equilibrium points, namely the uninfected equilibrium point and the infected
equilibrium point. We investigate the stability of both equilibrium points. Further we
examine the dynamical behavior of the system by finding a bifurcation point based
on the viral death rate and the number of new virions produced by infected CD4+
T-cells to investigate the influence of the fractional derivative on the HIV dynamics.
Finally numerical simulations are carried out to illustrate the analytical results.