Saturated lysing efficiency of CD8 cells induced monostable, bistable and oscillatory HIV kinetics.

Effector CD8 cells lyse human immunodeficiency viruses (HIV)-infected CD4 cells by recognizing a viral peptide presented by human leukocyte antigens (HLA) on the CD4 cell surface, which plays an irreplaceable role in within-host HIV clearance. Using a semi-saturated lysing efficiency of a CD8 cell, we discuss a model that captures HIV dynamics with different magnitudes of lysing rate induced by different HLA alleles. With the aid of local stability analysis and bifurcation plots, exponential interactions among CD4 cells, HIV, and CD8 cells were investigated. The system exhibited unexpectedly complex behaviors that were both mathematically and biologically interesting, for example monostability, periodic oscillations, and bistability. The CD8 cell lysing rate, the CD8 cell count, and the saturation effect were combined to determine the HIV kinetics. For a given CD8 cell count, a low CD8 cell lysing rate and a high saturation effect led to monostability to a high viral titre, and a low CD8 cell lysing rate and a low saturation effect triggered periodic oscillations; this explained why patients with a non-protective HLA allele were always associated with a high viral titer and exhibited bad infection control. On the other hand, a high CD8 cell lysing rate led to bistability and monostability to a low viral titer; this explained why protective HLA alleles are not always associated with good HIV infection outcomes. These mathematical results explain how differences in HLA alleles determine the variability in viral infection.