Caputo fractional-order modelling of HPV-induced cervical cancer progression under vaccination, screening and treatment controls

Cervical cancer is mainly associated with persistent infection by high-risk human papillomavirus (HPV) types and develops through a slow transition from infection to precancerous lesions and invasive disease. This multi-stage nature makes HPV-induced cervical cancer suitable for mathematical modeling. In this paper, we propose a Caputo fractional-order compartmental model describing HPV infection, precancerous progression and cervical cancer development under vaccination, screening and treatment controls. The population is divided into susceptible, vaccinated, HPV-infected, precancerous, cervical cancer and recovered classes. The Caputo fractional derivative is used to incorporate memory-dependent effects into the progression dynamics. Positivity and boundedness of solutions are established, and the disease-free equilibrium together with the basic reproduction number is derived by using the next-generation matrix method. Local stability is examined through the fractional-order stability criterion. In addition, an optimal control problem is formulated to evaluate the combined role of vaccination, screening and treatment in reducing infection and disease burden. Numerical simulations illustrate the effect of the fractional order and intervention strategies on the model dynamics. The results provide a mathematical basis for assessing integrated control policies against HPV-induced cervical cancer progression.