HIV infection dynamics with broadly neutralizing antibodies and CTL immune response

HIV infection remains a significant global public health concern. Although current antiretroviral therapies and broadly neutralizing antibodies (bNAbs) can decrease plasma viral load, they are unable to completely eradicate the virus. Alongside these treatments, the cytotoxic T lymphocyte (CTL) immune response also contributes to viral control. However, the impact of antiretroviral drugs and bNAb therapies on HIV dynamics in the presence of CTL immune responses remains uncertain. In this paper, we develop and analyze a mathematical model that incorporates CTL immune response, bNAb, and drug therapies. We demonstrate that the basic reproduction number $ \mathcal{R}_0 $ and the CTL immune response reproduction number $ \mathcal{R}_c $ determine the existence and stability of the equilibria. Numerical investigation reveals that both antiretroviral drugs and bNAb therapies can reduce the viral load to below the detection limit. However, bNAb therapy can delay the time to viral rebound compared with antiretroviral therapy alone. Furthermore, bNAbs have a more significant impact on viral reduction than the CTL immune response. The CTL immune response increases the number of uninfected cells and reduces the number of infected cells and viral load. Analysis of the relative contributions shows that bNAb therapy can enhance the CTL immune response, similar to the direct stimulation of antigens. These findings suggest that bNAb therapy, combined with CTL immune response, plays a critical role in HIV control and has important implications for understanding HIV pathogenesis and developing more effective treatment strategies to manage or even eliminate the disease.