Mathematical modeling of HBV–HDV transmission with superinfection: The role of vaccination and liver transplantation in disease dynamics

Hepatitis D virus (HDV) infection can substantially worsen the clinical outcomes of individuals infected with hepatitis B virus (HBV), making the prevention of HBV infection and the management of severe HBV–HDV cases important public-health priorities. This study introduces a novel mathematical model for Hepatitis B virus (HBV) and D virus (HDV) transmission, incorporating vaccination and liver transplantation as disease control strategies. In contrast to models that allow direct HDV infection or general coinfection pathways, the proposed model assumes that HDV occurs only through superinfection among individuals already infected with HBV. The model is constructed as a system of ordinary differential equations, where the human population is divided into susceptible, vaccinated, HBV-infected, recovered, chronic, and HDV-infected compartments. Model analysis reveals the existence and stability of the disease-free equilibrium, which exists and is asymptotically stable if the basic reproduction number ( ℛ 0 ) is less than one, and becomes unstable if it exceeds one. Two types of endemic equilibria are identified when ℛ 0 > 1 , corresponding to the absence and presence of HDV infection. Continuation analysis using MatCont reveals the existence of two branching points that govern the transition of stability between these equilibria, highlighting the conditions under which HDV emerges and persists. Global sensitivity analysis using Partial Rank Correlation Coefficient combined with Latin Hypercube Sampling indicates that vaccination coverage and vaccine efficacy play a dominant role in reducing ℛ 0 . Although liver transplantation does not affect the magnitude of ℛ 0 , it significantly influences the disease dynamics by reducing the outbreak size and delaying the timing of HBV and HDV outbreaks. These findings indicate that vaccination is essential for reducing transmission, whereas liver transplantation remains important for mitigating severe disease burden; thus, coordinated use of preventive and clinical interventions is needed for effective HBV–HDV control.