Studying the Role of Impulsive Antiviral Therapy for SARS-CoV-2 Treatment Using a Delay Induced Mathematical Model

Understanding how immune response delays influence the progression of SARS-CoV-2 infections is crucial for predicting disease progression and designing effective treatment strategies worldwide. So, this study proposes a mathematical model capturing the intrahost transmission dynamics of SARS-CoV-2 and investigates how delays in immune response affect disease progression using a new immune response function. Key model properties such as boundedness, non-negativity of solutions, and the basic reproduction number R0 are analyzed. The equilibrium points are derived, and their stability is examined under two scenarios: absence and presence of immune delay. It is shown that the disease-free state remains stable when R0 1, indicating a forward bifurcation at the threshold R0=1. Conditions under which Hopf bifurcation emerges are identified based on the length of delay. To address the destabilizing effects of immune delay, an impulsive control strategy is introduced. Appropriate dosing intervals and quantities for antiviral therapy are established to mitigate instability. Numerical simulations validate the analytical findings, revealing that critical delay values can induce periodic oscillations via Hopf bifurcation. Results of this study suggest that regular impulsive treatment can effectively manage cases with delayed immune activation.