Analysis of a mathematical model of human papillomavirus transmission dynamics with optimal control for cervical cancer prevention

This study presents a mathematical model that explains the transmission dynamics of high-risk Human Papillomavirus (HPV) and how it progresses to cervical cancer. The model particularly includes a population group for Cervical Intraepithelial Neoplasia (CIN), which is a critical precancerous stage that is usually neglected in previous models, and brings in a corresponding treatment compartment to fit realistic clinical interventions. Control measures such as vaccination, public campaign awareness, and regular screening are merged into the framework to analyze their unified impact on disease spread and cancer prevention. Using a system of non-linear differential equations, the model is assessed for positivity, boundedness, and stability. The basic reproduction number R o is computed using the next-generation matrix approach, and both local and global sensitivity analyses are carried out to determine the parameters that are most influential. An optimal control structure that is based on Pontryagin's Maximum Principle is applied to evaluate suitable intervention strategies. Simulation outcome reveals that increasing awareness and screening coverage can remarkably decrease both HPV infection and cervical cancer cases, especially in settings with inadequate vaccine coverage. This model provides practical insights for public health decision-making and strengthens the importance of integrated intervention in HPV-induced cervical cancer control.