Optimizing HPV Vaccination Strategy: An Optimal Control Problem

Human papillomavirus (HPV) is one of the most common sexually transmitted infections worldwide, with persistent infections by high-risk types such as HPV-16, 18, 31, 52, and 59 tightly linked to the development of cervical cancer. In response to this situation, vaccination has become a critical component of prevention strategies, especially in low-and middle-income countries where public health interventions may be limited. However, the difference in the impact of the disease between males and females and the financial constraints often necessitate sex-prioritized approaches, typically focusing on teenage girls. In this context, mathematical modeling and optimal control provide valuable tools to guide efficient vaccine allocation under resource limitations. Using a gender-stratified dynamic transmission model calibrated to Tunisian data, we investigate the impact of bivalent HPV vaccination on infection persistence and cancer incidence. The proposed model accounts for partial cross-immunity and captures both direct and indirect effects of female-only vaccination. An optimal control problem is formulated to minimize persistent infections and cancer cases while limiting vaccination effort, and is analysed using Pontryagin's Maximum Principle. Three vaccination scenarios are compared: an ideal case with full vaccine availability, and two resource-constrained cases with respective maximum coverage rates of 100% and 70%. The numerical simulations have revealed that the optimal strategy under ideal conditions can achieve remarkable suppression of infection, persistence, and cancer. Under constrained effort, the optimal control still achieves substantial reductions in disease burden, with minor differences in dynamics and speed of immunity buildup. Our results highlight the effectiveness of female-only HPV vaccination in providing both direct and indirect protection. They also emphasize the importance of sustained coverage in constrained settings.