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

Abstract

Human papillomavirus (HPV) vaccines have been introduced in several countries and have shown positive results in reducing HPV infection and related diseases. Nevertheless, immunization 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 associated 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 optimal 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 diseases 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 decrease vaccination rates.