Modeling of Hepatitis B Virus Transmission With Vaccination, Treatment, and Memory Effects

Abstract

This study presents a comprehensive fractional-order compartmental model to analyze the transmission dynamics of the hepatitis B virus (HBV), incorporating the impacts of vaccination, treatment, and memory effects. Utilizing Caputo fractional derivatives, the model captures the hereditary and memory characteristics inherent in biological systems, offering a more realistic depiction of disease progression. The population is divided into various compartments, representing various stages of infection, immunity, treatment, and recovery. The model's mathematical rigor includes the derivation of the basic reproduction number $R_0$, existence and uniqueness, and Hyers–Ulam stability of solutions. Sensitivity analysis highlights the influence of vaccination rate, recruitment rate, and vaccine efficacy on $R_0$, revealing complex interdependencies between acute and chronic stages of infection. Simulations demonstrate that lower memory $\eta$ accelerates transitions between compartments, affecting the timing and severity of infection peaks. The findings stress the importance of enhancing vaccine effectiveness, ensuring timely treatment, and strengthening diagnostic and educational interventions. The approach advances previous work by integrating non-standard compartments and analyzing their epidemiological roles. These integrated insights inform evidence-based strategies to control HBV transmission, minimize chronic carrier prevalence, and alleviate the long-term burden on healthcare systems.