Models for optimally controlling varicella and herpes zoster by varicella vaccination: a comparative study

The introduction of mass vaccination against Varicella-Zoster-Virus (VZV) is being delayed in many European countries mainly because of the "fear" of a subsequent boom in natural herpes zoster (HZ) incidence in the first decades after the initiation of vaccination, caused by the expected decline in the protective effect of natural immunity boosting due to reduced virus circulation. Optimal control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases by devising the optimal disease intervention strategies. In this paper, we describe how a reduced 'toy' model can extract the essentials of the dynamics of the VZV transmission and reactivation in case of the study of optimal paths of varicella immunization programs. Results obtained using different optimization approaches are compared with the ones of a more realistic age-structured model. The reduced model shows some unreliable predictions in regards of model time scales about herpes zoster dynamic; nevertheless, it is able to reproduce the main qualitative dynamic of the more realistic model to the different optimization problems, while requiring a minimal number of parameters to be identified.