Vaccination strategies in a pair formation model for human papillomavirus infection: An optimal control approach

Human papillomavirus (HPV) infection is a widespread sexually transmitted infection responsible for several cancers including anal, oropharyngeal, penile, vaginal, and cervical cancer. Despite HPV vaccines have been available for almost 20 years and are incredibly effective in preventing infection, the scale-up of vaccination has been slow in many low and middle-income countries. This analysis uses a pair model that explicitly accounts for sexual partnership formation to investigate HPV immunization programs. The optimality of vaccine interventions is analyzed using optimal control theory. We give formal proof of the existence of optimal control solutions and obtain first-order optimality conditions via Pontryagin's Maximum Principle. Extensive numerical simulations are used to investigate plausible what-if scenarios to understand under which conditions the inclusion of males should be recommended in addition to female vaccination. The results suggest that a gender-neutral vaccination program should be recommended in regions where vaccination uptake in women is still low whereas for an already existing female-only program with high uptake, it is more effective to keep increasing coverage in females.