This article focuses on the infection dynamics of a fractional-order HIV/AIDS model, incorporating antibodies and cytotoxic T-lymphocyte immune responses. Our model accounts for both modes of transmission of the infection, which are: virus-to-cell and cell-to-cell, while also including the CD \(4^{+}\) T cell latent reservoir. The model includes the latent period as a new variable representing the concentration of latently infected cells, which contain the virus but do not produce it. This work examines the qualitative behavior of virus dynamics in terms of global stability analysis of the equilibria. To perform the theoretical analysis of global stability, we utilize a numerical approach based on the fundamental theorem of fractional calculus combined with a four-step Lagrange polynomial interpolation method. We conclude the numerical tests confirm the stability of all steady states under certain optimal conditions, aligning with the theoretical findings. Among the results obtained, we give those of the integer-order model to compare the impact of fractional-order derivatives in the HIV infection model.
