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.