Impulsive Antibody Therapy for Hopf Bifurcation Control in Human SARS-CoV-2 Dynamics

This work develops and analyzes a mathematical model of SARS-CoV-2 infection within the human host, incorporating 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 ( mathcal{R}_0 < 1 ), while an endemic equilibrium arises for ( mathcal{R}_0 > 1 ). To capture therapeutic intervention, an impulsive control framework based on antibody-mediated drug administration is introduced. Within this framework, the existence and stability of a disease-free periodic orbit are established through the impulsive reproduction number, ( mathcal{R}_0^{imp} ), with stability ensured when ( mathcal{R}_0^{imp} < 1 ). Numerical simulations confirm the analytical results, demonstrating the effectiveness of impulsive therapy in achieving viral eradication. Additionally, Hopf bifurcating periodic solutions are observed under elevated viral replication and infection rates. The proposed model provides new insights into the interaction between viral dynamics, immune response, and impulsive therapeutic strategies, offering a rigorous foundation for advancing treatment approaches against SARS-CoV-2.