Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses

Abstract

The present study discussed a model to describe the SARS-CoV-2 viral kinetics in the presence of saturated antiviral responses. A discrete-time delay was introduced due to the time required for uninfected epithelial cells to activate a suitable antiviral response by generating immune cytokines and chemokines. We examined the system's stability at each equilibrium point. A threshold value was obtained for which the system switched from stability to instability via a Hopf bifurcation. The length of the time delay has been computed, for which the system has preserved its stability. Numerical results show that the system was stable for the faster antiviral responses of epithelial cells to the virus concentration, i.e., quick antiviral responses stabilized patients' bodies by neutralizing the virus. However, if the antiviral response of epithelial cells to the virus increased, the system became unstable, and the virus occupied the whole body, which caused patients' deaths.

Keywords

• mathematical modeling
• sars-cov-2
• time delay
• stability
• hopf bifurcation
• numerical simulations