Using their model, the team determined how many individuals in the model population had to be vaccinated in order to eliminate a disease. They found that this “critical ratio” was the same for all three types of imperfect vaccines. When vaccination coverage was less than this critical ratio–which can change depending on the protection level provided by the vaccine and how a disease spreads–the disease remained at large. Surprisingly, however, the model found that leaky vaccines led to higher infection rates in the population than all-or-nothing or waning vaccines.