Identifying Critical Viral Load Thresholds in HBV-HDV Superinfection: A Mathematical Modelling Approach

Approximately 254 million people live with hepatitis B virus (HBV) globally, with 12 million having hepatitis D virus (HDV) coinfection [1]. While research suggests HBV viral load influences HDV superinfection risk [2], the precise relationship remains poorly understood. This paper proposes a mathematical model to identify critical viral load thresholds determining HDV superinfection probability. We develop a six-dimensional system of ordinary differential equations incorporating susceptible, HBV-infected, HDV-coinfected, under-treatment, recovered, and viral load compartments [5]. A novel feature is the inclusion of a continuous viral load-dependent probability function for HDV superinfection, implemented through a sigmoidal threshold. Using next-generation matrix methodology [3], we derive basic reproduction numbers and identify three equilibrium states. Stability and bifurcation analyses reveal that HDV superinfection probability remains low below an HBV viral load threshold of ~10^5 IU/mL but exceeds 80% above 10^8 IU/mL. Model simulations calibrated with WHO 2024 data [1] suggest early HBV viral load suppression (within 6 months of infection) can reduce HDV superinfection risk by up to 60%, whereas delayed treatment (beyond 12 months) results in chronic coinfection in over 70% of cases. Sensitivity analysis indicates that lowering HBV viral load by one log unit can decrease HDV transmission rates by 30-40%. This mathematical framework provides testable hypotheses for HDV superinfection thresholds and offers insights for optimizing treatment timing [2]. These findings have direct implications for clinical strategies in managing HBV-HDV coinfection.