When optimal is not the best: cost effectiveness analysis for HPV epidemic models

This paper aims to evaluate the potential cost-effectiveness of healthcare interventions against human papillomavirus (HPV). For this, we consider a two-sex epidemic model for the transmission dynamics of HPV which includes screening, vaccination of adolescent boys and girls, and vaccination of sexually active adults. We first propose public health policies using constant control parameters and develop a cost-effectiveness analysis (CEA) to identify which intervention delivers the best effectiveness for the money invested. Secondly, we consider time-dependent control parameters and formulate an optimal control problem to obtain time-dependent versions of the interventions. As in the case of constant control parameters, we perform a CEA to investigate the cost-effectiveness of the time-dependent control interventions. Our findings suggest that females' vaccination, including adolescent girls and adult women, is the most cost-effective strategy. We also compare constant against the time-dependent healthcare interventions which are optimal in the sense that they minimize the objective functional of the optimal control problem. The results indicate that time-dependent controls are not always more cost-effective than constant controls.