Analyzing the dynamics of human papillomavirus transmission via fractal and fractional dimensions under Mittag-Leffler Law

The human papillomavirus (HPV) is a common sexually transmitted infection and a leading cause of cervical cancer. The yearly hospitalization rate for diseases linked to HPV is alarming. However, the mathematical study of HPV disease using fractal-fractional derivatives has received less attention from researchers globally. In this study, we develop a compartmental model of HPV transmission dynamics that includes a hospitalized compartment. We investigate the dynamics of our model equations through fractal and fractional analysis using the Mittag-Leffler law. The fractional order enables us to capture the memory effects, and the fractal dimension helps to capture self-similarities in the HPV model. The fixed point theorem is employed to establish the existence and uniqueness of solutions for the proposed fractal-fractional model. We conduct a stability analysis utilizing Hyers-Ulam criteria to demonstrate that the model's equation exhibits robust and stable behavior. A novel numerical scheme is discussed and the numerical simulations are conducted using this proposed scheme. The simulation results reveal that the fractal dimension and fractional order significantly influence the dynamics of the HPV fractal-fractional model. Both factors substantially affect the model's trajectories, as demonstrated by numerical simulations. Moreover, higher fractional order and fractal dimension values lead to a decrease in individuals across the different compartments as the simulation progresses. The numerical simulations illustrate the need to employ fractal-fractional derivatives in studying infectious diseases like HPV. For researchers and other interested stakeholders, we recommend modeling the coinfection of HPV and other sexually transmitted diseases in future extensions.