Fig. 2

Types of vaccine effectiveness, as developed by Halloran et al. [34]. Cluster 1 has a fraction of the population vaccinated, while cluster 2 has no person vaccinated. The u and v indices designate vaccinated and unvaccinated people, respectively. Direct effectiveness compares the attack rate (AR) (or some other rate measure, e.g. incidence) of vaccinated to unvaccinated people within a cluster, as in cluster 1. Indirect effectiveness compares the AR in unvaccinated people in the partially vaccinated cluster 1 to the AR in an unvaccinated cluster 2. Total effectiveness compares the AR of vaccinated people in cluster 1 to the AR in cluster 2. Finally, overall effectiveness compares the AR among all people in cluster 1 (i.e. vaccinated and unvaccinated) to the AR among all people in cluster 2