Mathematical Analysis of an Optimal Control Problem for Mitigating HPV Transmission and Cervical Cancer Progression through Educational Campaigns

Abstract

Human papillomavirus (HPV) is a sexually transmitted infection that affects the cervix (the lower part of the uterus leading to the vagina) and is often associated with cervical cancer. This paper introduces a control-induced deterministic model to analyze and combat the spread of HPV and cervical cancer in India. We establish the nonnegativity and boundedness of the solution of the model and also provide the basic reproduction number \(\mathcal {R}_0\). The existence of equilibria in the model is determined. An objective functional is formulated to reduce HPV and cervical cancer infections by raising awareness among the susceptible population through educational campaigns. The existence of the optimal control is proved, and the necessary conditions for the optimality system are derived. Utilizing Pontryagin’s maximum principle, we explicitly formulate the optimal control. Through numerical simulations, we elucidate the pivotal role of the control variable: that is, its absence leads to \(\mathcal {R}_0 > 1\), indicative of sustained disease transmission, while its inclusion reduces \(\mathcal {R}_0 < 1\), signaling a decline in outbreaks. Notably, varied control variable values exert substantial influence on the model dynamics. The stability of equilibria is established graphically. Moreover, the obtained findings underscore the efficacy of educational campaigns in mitigating HPV spread, offering promising avenues for disease control and prevention.