Modeling the transmission dynamics and vaccination strategies for human papillomavirus infection: An optimal control approach

Human papillomavirus (HPV) vaccines have been introduced in several countries and have shown positive results in reducing HPV infection and related diseases. Nevertheless, im-munization programs remain sub-optimal and more effort is needed to design efficient vaccination deployment. We formulate a two-sex deterministic mathematical model that incorporates the most important epidemiological features of HPV infection and associ-ated cancers. To assess the population-level impact of HPV immunization programs, the model incorporates school-based vaccine delivery for juveniles and catch-up vaccination for adults. The dynamics of the model are rigorously analyzed using the next-generation operator, the center manifold theorem, and normal forms theory. We formulate an optimal control problem to determine the best deployment strategy for HPV vaccination for several plausible scenarios. We establish the existence of solutions of the optimal control problem, and use Pontryagin's Maximum Principle to characterize the necessary conditions for op-timal control solutions. The findings suggest that if girls-only programs are complemented with catch-up vaccination for adult females, such program has the potential to achieve HPV-associated cancers eradication even if boys and males do not receive the vaccine. We also find that the optimal vaccine deployment, in terms of minimizing HPV associated dis-eases and the cost of vaccination, is to allocate as much vaccines as possible at the initial phase of the epidemic and once a high vaccination coverage is reached then gradually de-crease vaccination rates.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

HPV vaccines have shown positive results in reducing HPV infection and related diseases. This study presents a mathematical model to assess the impact of HPV immunization programs and determine the optimal deployment strategy for vaccination. The findings suggest that girls-only programs complemented with catch-up vaccination for adult females can achieve HPV-associated cancers eradication. The optimal vaccine deployment is to allocate more vaccines in the initial phase of the epidemic and then gradually decrease vaccination rates.