Papillomaviruses are microorganisms belonging to the Papillomaviridae family that primarily target skin and mucous membrane cells. They are responsible for numerous public health issues worldwide. According to the World Health Organization, these viruses cause various diseases, including precancerous lesions that can develop into different types of cancers.

To better control, or even eradicate, the spread of these viruses, this work proposes a general model of human papillomavirus (HPV) transmission. The model incorporates a therapeutic intervention aimed at correcting immune system deficiencies and reducing the risk of viral spread.

The mathematical analysis conducted demonstrates that the model’s solution is stable, positive, and bounded, meaning the results are realistic and reliable.

By applying control theory, combined with a mathematical method known as Pontryagin’s Maximum Principle, this work has identified the optimal strategy for therapeutic intervention. Simulations clearly show that adopting an effective treatment strategy could lead to a significant reduction in infections within the population. Furthermore, the obtained results could be used to predict the epidemiological evolution of infections, thereby aiding in the development of preventive policies.