Qualitative stability and semi-analytical solutions of fractional-order hepatitis B model under Riemann–Liouville fractional derivative

Mathematical models aid in understanding and managing infectious diseases by providing data for decision-making, evaluating interventions, and predicting spread; this study conducts an in-depth qualitative and semi-analytical analysis of a hepatitis B virus (HBV) transmission model using the Riemann–Liouville fractional derivative, which better captures memory effects and non-local interactions compared to integer-order models. Fixed point theory establishes the existence and uniqueness of solutions through Lipschitz conditions on kernel functions, while the homotopy decomposition method (HDM) combined with the Cauchy n-integral formula yields efficient semi-analytical solutions without discretization or restrictive assumptions. MATLAB simulations validate these solutions and reveal that lower fractional orders delay the infection peak, reduce chronic carrier density, and suggest enhanced control via early intervention, offering valuable insights for clinical practices, vaccination strategies, and healthcare system improvements.