A dynamical analysis of fractional order hepatitis B virus transmission model with vaccine effects

A fractional-order mathematical model of the hepatitis B virus (HBV) consisting of eight distinct compartmental classes, is developed and dynamically analysed in this paper. Using the Banach fixed-point theorem, we rigorously establish the existence and uniqueness of the exact solution. The Routh–Hurwitz criteria and Lyapunov functions are employed to demonstrate the local and global stability of the infection-free equilibrium, respectively. A total of 200 iterations are performed using Latin hypercube sampling with partial rank correlation coefficients, taking the basic reproduction number as the response function. In simulations, lowering the fractional order noticeably softened the infection peaks. When the order was reduced to η=0.75, the infected groups reached their maximum levels sooner and with much smaller intensities compared to the case η=1. This demonstrates how incorporating memory effects into the model can naturally slow the spread of HBV and lessen the severity of outbreaks.