Perspectives on optimal control of varicella and herpes zoster by mass routine varicella vaccination

Herpes zoster arises from reactivation of the varicella\textendashzoster virus (VZV), causing varicella in children. As reactivation occurs when cell-mediated immunity (CMI) declines, and there is evidence that re-exposure to VZV boosts CMI, mass varicella immunization might increase the zoster burden, at least for some decades. Fear of this natural zoster boom is the main reason for the paralysis of varicella immunization in Europe. We apply optimal control to a realistically parametrized age-structured model for VZV transmission and reactivation to investigate whether feasible varicella immunization paths that are optimal in controlling both varicella and zoster exist. We analyse the optimality system numerically focusing on the role of the cost functional, of the relative zoster\textendashvaricella cost and of the planning horizon length. We show that optimal programmes will mostly be unfeasible for public health owing to their complex temporal profiles. This complexity is the consequence of the intrinsically antagonistic nature of varicella immunization programmes when aiming to control both varicella and zoster. However, we show that gradually increasing\textemdashhence feasible\textemdashvaccination schedules can perform better than routine programmes with constant vaccine uptake. Finally, we show the optimal profiles of feasible programmes targeting mitigation of the post-immunization natural zoster boom with priority.