Investigation of stability criteria and optimal control measures for a fractional-order model of human papillomavirus infection and cervical cancer

This paper presents a mathematical formalism with the Liouville–Caputo fractional derivative (LCFD) to investigate the transmission dynamics of Human papillomavirus (HPV) infection and related cervical cancer. The proposed fractional-order model (FOM) is designed through six fractional differential equations (FDEs), each equation capturing different compartments of individuals as well as the most important epidemiological features of HPV infection and related cervical cancer. We illustrate the solutions existence, positivity, uniqueness and boundedness to verify the well-posedness of this FOM. The basic reproduction number ([Formula: see text]) is evaluated to show whether the infection is growing in a population or not. Moreover, we demonstrate the stability analysis for disease-free equilibrium and endemic equilibrium points (EPs). A sensitivity analysis is conducted to identify key epidemiological parameters. The fractional optimal control problem (FOCP) is formulated using an objective function that incorporates three time-dependent control variables, each representing realistic interventions, namely [Formula: see text] represents measures promoting safe sexual practices, [Formula: see text] represents HPV prevention strategies, including vaccination and immunity enhancement, and [Formula: see text] represents cervical cancer prevention methods, such as regular screenings and medications to inhibit cancerous cell development. The necessary optimality conditions (NOCs) for this FOCP are derived using Pontryagins Maximum Principle (PMP). Four different control strategies resulting from a combination of the proposed controls are presented. The numerical simulations presented reveal that each strategy can reduce HPV infection and cervical cancer to some extent, however, the combination of the three controls gives the best scenario for controlling HPV infection and cervical cancer. It was also shown that the fractional operator plays a pivotal role in controlling the disease in addition to suggested controls.