Assessing the Impact of Multi-Level Clinical Interventions and Safe Practices Compliance for Hepatitis B Transmission: A fractional-Order Model Approach

Hepatitis B remains a major public health concern worldwide, particularly in developing nations where poor vaccination coverage, lack of screening, unsafe sexual practices, and delayed treatment fuel its spread. We developed a fractional-order model incorporating vaccination, screening, post-exposure prophylaxis (PEP), acute and chronic infection management, and behavioural measures. Theoretical analysis confirmed the model's existence, uniqueness, positivity, and boundedness. Equilibrium states were identified, and the basic reproduction number (R₀) was derived via the next-generation matrix. The disease-free equilibrium is locally and globally asymptotically stable when R₀< 1, while the endemic equilibrium exists and is globally asymptotically stable when R₀>1. Model fitting and parameter estimation used acute Hepatitis B data from Ireland. Sensitivity analysis identified vaccination, screening, and safe practices as the most influential control factors. Numerical simulations showed that conventional strategies alone are insufficient; higher vaccination coverage, efficient screening, improved safe practices, and effective PEP are essential to reduce transmission. Collectively, these interventions minimize progression to chronic disease, reduce long-term burden, lower complications and mortality, particularly when acute infection management is included.