Fractional gender structured model of human papillomavirus (HPV).

We propose a fractional-order differential equation model to study the gender-specific transmission dynamics of human papillomavirus (HPV). Due to limited gender-disaggregated HPV data, oropharyngeal cancer incidence was used as a proxy. The model includes a theoretical analysis of disease-free and endemic equilibria and computation of the basic reproduction number, with stability conditions derived for both cases. Structural identifiability was confirmed using differential algebra, and data fitting indicated that the fractional models $ (\alpha = 0.9) $ better captured U.S. dynamics, while classical models $ (\alpha = 1) $ suited Turkish data. Practical identifiability, assessed via Monte Carlo simulations, revealed that most parameters were identifiable, though some (e.g., the male exit rate $ \mu_m $) showed limitations. Numerical simulations demonstrated sensitivity to fractional effects. This work provides a robust framework for modeling the transmission of HPV and offers insights for future epidemiological modeling and intervention planning.