Numerical Simulation of Transmission Dynamics of the HBV Model of Fractional-Order via a Generalized Runge–Kutta Method

This study presents a fractional-order SEAIR model for the transmission dynamics of Hepatitis B, incorporating Caputo derivatives to account for memory effects in disease progression. The model is analyzed both theoretically and numerically using the generalized Runge–Kutta method of fourth order (GRK4M). Analytical results demonstrate the existence and uniqueness of solutions, and provide conditions for the stability of both local and global equilibria. Numerical simulations, performed over a long time interval horizon with biologically feasible initial conditions and epidemiologically validated parameters, show convergence to their equilibrium states for varying fractional orders, highlighting the role of memory effects in delaying transitions between disease stages. Fractional-order dynamics represent compartmental stages more accurately than classical integer-order models. Sensitivity analyses indicate that transmission-related parameters critically affect infection prevalence, emphasizing the importance of early detection, treatment, and quarantine measures in controlling disease spread. Overall, the fractional SEAIR model, coupled with GRK4M, provides a robust tool for understanding Hepatitis B dynamics and designing effective intervention strategies.