Hepatitis B virus (HBV) infection remains a major health challenge due to the persistence of covalently closed circular DNA (cccDNA), which acts as a reservoir for viral replication and hinders complete cure. Existing mathematical models have offered valuable insights into HBV dynamics, but the independent role of cccDNA recycling has not been clearly isolated, as most studies embed these processes within complex immune responses or therapy-focused frameworks. To address this gap, we developed a mathematical model that distinguishes between hepatocytes carrying single and multiple copies of cccDNA, thereby capturing intracellular heterogeneity that is often overlooked. Using a system of four differential equations, we derived the basic reproduction number (R0) through the next-generation matrix method and analyzed the stability of both disease-free and endemic equilibria. Numerical simulations, including bifurcation and sensitivity analyses, were conducted to evaluate the impact of key parameters on HBV persistence. The results demonstrate that the recycling parameter associated with single-copy cccDNA plays a dominant role in reducing HBV persistence compared to transitions involving multiple-copy states. These findings underscore the importance of accounting for cccDNA burden at the cellular level and provide theoretical insights that may guide the design of antiviral strategies targeting early infection stages.