Fractional modeling of hepatitis B virus transmission via heterosexual and homosexual contacts and its disability burden

The hepatitis B virus (HBV) is a major public health problem worldwide. Sexual intercourse, heterosexual and homosexual, is an important factor in HBV transmission in adults. This study develops a fractional-order mathematical model to describe the spread of HBV, using fractional calculus with a Mittag-Leffler kernel to account for memory effects and hereditary properties of biological systems. The adult population is divided into the groups of susceptible, infected, carrier, and recovered, on the basis of sex and sexual habits. The model incorporates HBV-related disability using gender-specific probabilities that capture long-term functional impairments among carriers. We derive the basic reproduction number (R₀) and analyze the disease-free equilibrium (E₀). Theoretical results include conditions ensuring existence and uniqueness of solutions and the Hyers-Ulam stability of the system. Sensitivity analysis of R₀ identifies infection rates among same-sex partners, contact frequency, and immunity levels as major factors influencing HBV dynamics. Numerical simulations based on the generalized Mittag-Leffler kernel illustrate the model's behavior over time. The findings suggest that strengthening immunization programs, reducing the number of carriers, and promoting safe sexual practices can effectively control HBV transmission. The study highlights the value of fractional-order models for capturing complex disease processes and evaluating long-term health outcomes within affected populations.