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.