Dynamic analysis of human papillomavirus transmission model under vaccine intervention: a case study of cervical cancer patients from Hungary

Nearly 80% of women are estimated to have at least one HPV infection from high-risk types. Although the majority can clear the infection through their immune system, some are at risk for cervical cancer. Persistent high-risk HPV infections are the leading cause of cervical cancer worldwide. This paper proposes a mathematical model that examines the effects of HPV transmission on cervical cancer patients under vaccine intervention. The model’s fundamental properties are investigated, including the stability of equilibrium points and the existence of forward bifurcations. Subsequently, based on cervical cancer patient data collected from Hungary between 2000 and 2020, the model’s optimal parameter values are identified using a nonlinear least squares method. Further, we perform a sensitivity analysis of the key cervical cancer progression parameters. Our results indicate that both direct HPV vaccination in susceptible populations and additional vaccination in individuals who have recovered can improve immune responses and reduce the risk of cervical cancer. In addition, the study of the effects of intervention measures on cervical cancer patients in Hungary from 2000 to 2030 reveals that reducing the contact rate is conducive in the short term to curbing the development of cervical cancer; however, in the long term, relying solely on this measure is not sufficient to lead to a significant decrease in the number of cervical cancer cases.