Topological Stability and Transcritical Bifurcations in a Target-Cell-Limited Model of HBV-HDV Viral Interference

While minimalist kinetic models effectively capture the acute inverse coupling between Hepatitis B (HBV) and Hepatitis Delta (HDV), they often fail to account for the asymptotic stability and long-term viral plateaus observed during clinical therapy. In this work, we present an expanded compartmental framework integrating the non-linear dynamics of susceptible (S) and infected (I) hepatocyte populations, explicitly incorporating the satellite nature of HDV. Using the next-generation matrix method and Lyapunov stability theory, we analytically derive R₀ and prove the global attractivity of the endemic equilibrium. We demonstrate that "Target Cell Limitation" serves as the fundamental homeostatic governor. A transcritical bifurcation at threshold drug efficacy ε ≈ 0.9 marks the mathematical boundary between chronic persistence and viral extinction.