A Modified Fractional-Order SEICRV Model for Hepatitis B Virus Qualitative Analysis and a Laplace-Adomian Decomposition Solution

Abstract

A modified fractional-order model for Hepatitis B virus (HBV) transmission is proposed. The formulation extends a classical SEICR-type structure by introducing an explicit vaccinated compartment, waning of vaccine-induced immunity, and a carrier-directed treatment mechanism. The system is described using Caputo fractional derivatives in order to incorporate memory effects inherent in epidemic processes.The positivity and boundedness of solutions are established within a biologically feasible invariant region. The disease-free equilibrium is derived, and the basic reproduction number R0is obtained using the next-generation matrix approach. Furthermore, a Laplace–Adomian Decomposition Method (LADM) is constructed for the resulting nonlinear fractional system, including explicit Adomian polynomials for the bilinear infection terms. Numerical results for representative fractional orders illustrate the influence of memory effects on the solution profiles and demonstrate the added flexibility of the fractional-order framework compared to the classical integer-order model.