Impulsive Antibody Therapy and Hopf Bifurcation Analysis in SARS-CoV-2 Dynamics

In this article, we formulated a mathematical model to describe SARS-CoV-2 development in humans, accounting for the dynamics of susceptible and infected epithelial cells, viral particles, ACE2 receptors, cytotoxic T lymphocytes (CTLs), and antibodies. The basic reproduction number and equilibrium points are derived, with stability analysis showing that the disease-free equilibrium is maintained when R0<1, while an endemic equilibrium arises for R0>1. Additionally, Hopf bifurcating periodic solutions are observed under elevated viral replication and infection rates. To capture therapeutic intervention, an impulsive control framework based on antibody-mediated drug administration is introduced. The existence and stability of a disease-free periodic orbit are established through the impulsive reproduction number R0imp, with stability ensured when R0imp<1. The findings from numerical simulations support the analytical outcomes, proving the efficacy of impulsive control in suppressing viral persistence. The current research work offers important knowledge on the interaction between immune system and impulsive control mechanisms, which serves as a basis to develop therapies against SARS-CoV-2.