Delay induced stability switch in a mathematical model of CD8 T-cell response to SARS-CoV-2 mediated by receptor ACE2

The pathogen SARS-CoV-2 binds to the receptor angiotensin-converting enzyme 2 (ACE2) of the target cells and then replicates itself through the host, eventually releasing free virus particles. After infection, the CD8 T-cell response is triggered and appears to play a critical role in the defense against virus infections. Infected cells and their activated CD8 T-cells can cause tissue damage. Here, we established a mathematical model of within-host SARS-CoV-2 infection that incorporates the receptor ACE2, the CD8 T-cell response, and the damaged tissues. According to this model, we can get the basic reproduction number R0 and the immune reproduction number R1. We provide the theoretical proof for the stability of the disease-free equilibrium, immune-inactivated equilibrium, and immune-activated equilibrium. Finally, our numerical simulations show that the time delay in CD8 T-cell production can induce complex dynamics such as stability switching. These results provide insights into the mechanisms of SARS-CoV-2 infection and may help in the development of effective drugs against COVID-19.