Optimal control with multiple human papillomavirus vaccines

A two-sex, deterministic ordinary differential equations model for human papillomavirus (HPV) is constructed and analyzed for optimal control strategies in a vaccination program administering three types of vaccines in the female population: a bivalent vaccine that targets two HPV types and provides longer duration of protection and cross-protection against some non-target types, a quadrivalent vaccine which targets an additional two HPV types, and a nonavalent vaccine which targets nine HPV types (including those covered by the quadrivalent vaccine), but with lesser type-specific efficacy. Considering constant vaccination controls, the disease-free equilibrium and the effective reproduction number RvRv for the autonomous model are computed in terms of the model parameters. Local-asymptotic stability of the disease-free equilibrium is established in terms of RvRv. Uncertainty and Sensitivity analyses are carried out to study the influence of various important model parameters on the HPV infection prevalence. Assuming the HPV infection prevalence in the population under the constant control, optimal control theory is used to devise optimal vaccination strategies for the associated non-autonomous model when the vaccination rates are functions of time. The impact of these strategies on the number of infected individuals and the accumulated cost is assessed and compared with the constant control case. Switch times from one vaccine combination to a different combination including the nonavalent vaccine are assessed during an optimally designed HPV immunization program.