Numerical Optimization and Sensitivity Analysis of a Fractional-Order HBV Transmission Model Under Varying Vaccination and Memory Parameters

Abstract

This study presents a fractional-order SVICR (Susceptible–Vaccinated–Infected–Carrier–Recovered) model for analyzing the transmission dynamics of the Hepatitis B Virus (HBV), utilizing the Atangana–Baleanu–Caputo (ABC) operator to account for memory dependent biological processes. The model integrates key epidemiological features including vertical and horizontal transmission, vaccination coverage, waning immunity, and chronic carrier states. Using the fractional-order formulation, we derive a nonlinear system of differential equations and employ the Adams–Bashforth–Moulton predictor– corrector scheme for numerical simulations. Model calibration and sensitivity analysis are conducted through partial rank correlation coefficients (PRCC) and Latin Hypercube Sampling (LHS) to evaluate the impact of fractional order, vaccination rate, and transmission parameters on the basic reproduction number R0R_0. Simulation results demonstrate that lower fractional orders delay epidemic peaks while reducing infection amplitude, and that vaccination significantly suppresses transmission but is insufficient for eradication due to persistent vertical transmission and carrier states. Bifurcation analysis reveals the possibility of backward bifurcation under memory effects, emphasizing the need for combined vaccination, maternal screening, and carrier monitoring strategies. The model is validated against synthetic epidemiological data with low prediction errors, confirming its robustness and applicability. This research underscores the importance of fractional calculus in modeling chronic infectious diseases and provides a powerful tool for optimizing public health interventions in memory driven epidemiological systems.