Optimal Varicella immunization programs for both Varicella and Herpes Zoster Control

A main obstacle to the widespread adoption of varicella immunization in Europe has been the fear of a subsequent boom in natural herpes zoster caused by the decline in the protective effect of natural immunity boosting due to reduced virus circulation. We apply optimal control to simple models for VZV transmission and reactivation to investigate existence and feasibility of temporal paths of varicella childhood immunization that are optimal in controlling both varicella and zoster. We analyze the optimality system numerically focusing on the role played by the structure of the cost functional, the relative cost zoster-varicella, and the length of the planning horizon. We show that optimal programs exist but will mostly be unfeasible in real public health contexts due to their complex temporal profiles. This complexity is the consequence of the intrinsically antagonistic nature of varicella immunization programs when aimed to control both varicella and herpes zoster. However we could show that gradually increasing, smooth – thereby feasible - vaccination schedules, can perform largely better than routine programs with constant vaccine uptake. Moreover we show the optimal temporal profiles of feasible immunization programs targeting with priority the mitigation of the post-immunization natural zoster boom