High immunization rates are often sought to contain epidemics with target values typically 70% or greater. Our objective is to independently assess this value in the context of the 2020 Covid-19 pandemic in French Polynesia. To this extent, we develop a graph-based epidemic model tailored to this pandemic and compute the vaccination threshold required to prevent exponential spread of the communicable disease. Our results indicate that herd immunity increases drastically when a threshold percentage of vaccinated individuals is reached. Experimental data using our idealized model indicates that the threshold value is approximately 45%. We conclude that vaccination is much more effective at preventing pandemics than usually predicted.