Mathematical analysis of a human papillomavirus transmission model with vaccination and screening

We formulate a mathematical model to explore the transmission dynamics of human papillomavirus (HPV). In our model, infected individuals can recover with a limited immunity that results in a lower probability of being infected again. In practice, it is necessary to revaccinate individuals within a period after the first vaccination to ensure immunity to HPV infection. Accordingly, we include vaccination and revaccination in our model. The model exhibits backward bifurcation as a result of imperfect protection after recovery and because the basic reproduction number is less than one. We conduct sensitivity analysis to identify the factors that markedly affect HPV infection rates and propose an optimal control problem that minimizes vaccination and screening cost. The optimal controls are characterized according to Pontryagin's maximum principle and numerically solved by the symplectic pseudospectral method.