The main aim of this study is to analyze the dynamical properties of hepatitis B-type virus (HBV) infection in terms of mathematical model. The presented mathematical model on HBV involves the various factors such as immune impairment, total carrying capacity, logistic growth term, and antiretroviral therapies. In addition, the effect of time delays is also considered into the model, which are inevitable during the activation of immune response and time taken to infect the healthy cells. Mathematically, the qualitative analyses such as stability, bifurcation, and stabilization analysis are performed to explore the dynamical characteristics of HBV over the period of time. The significance of the model parameters is revealed through Hopf-type bifurcation analysis and the global stability analysis of the proposed model. With the help of data set values that are extracted from the literature, the efficiency of the derived theoretical results is explored. © 2021 John Wiley & Sons, Ltd.