Mathematical modeling is crucial in investigating the pandemic of the ongoing coronavirus disease (COVID-19). The primary target area of the SARS-CoV-2 virus is epithelial cells in the human lower repertory track. During this viral infection, infected cells can initiate innate and adaptive immune responses to viral infection. Immune response in COVID -19 infection can lead to longer recovery time and more severe secondary complications. We formulate a target cell limited mathematical model by incorporating a saturation term for SARS-CoV-2 infected epithelial cell loss reliant on infected cell levels. Forward and backward bifurcation between disease-free and endemic equilibrium points has been analyzed. Global stability of both disease-free and endemic equilibrium is provided. We have seen that the disease-free equilibrium is globally stable for $R_0<1$, and endemic equilibrium exists and is globally stable for $R_0>1$. Impulsive application of drug dosing has been applied for the treatment of covid-19 patients. Also, the dynamics of the impulsive system are discussed when a patient takes drug holidays. The numerical simulations are performed in support of our analytical findings and for the qualitative analysis of the system's dynamics with and without impulse drug dosing.