A mathematical analysis of human papilloma virus (HPV) disease with new perspectives of fractional calculus

The human papilloma virus (HPV) presents a significant global public health challenge, especially in regions with limited access to healthcare and preventive measures. This study introduces a novel mathematical model to analyze the transmission dynamics of HPV infection, incorporating advanced fractional calculus techniques. Unlike previous models, this framework integrates vaccination strategies, carrier dynamics, and reinfection phenomena through the innovative use of the piecewise Atangana–Baleanu derivative within the Caputo definition framework. The study key contributions includes establishing the existence and uniqueness theory, investigating Ulam–Hyers stability, and identifying equilibrium points for the proposed model. Furthermore, the work extends numerical methods by applying an Adams-type predictor–corrector scheme for Atangana–Baleanu derivatives and adapting the Adams–Bashforth–Moulton method for Caputo derivatives to achieve precise computational results. Through a detailed numerical analysis, the model explores the impact of varying fractional-order values on HPV transmission dynamics, providing insights into how fractional-order systems can better capture the complex interactions and interconnectedness of communities. These advancements highlight the novelty of the approach in improving disease modeling and enhancing the understanding of HPV transmission.