THEORY: Assuming 100% efficacy vaccine. In completely homogeneous population if people are randomly vaccinated the threshold where the diseases effective R drops below 1.0 is 1 - 1/R. For example if R = 3.0 you need to vaccinate 66% population until infections start to decline.

REALITY: Assuming 75-90% efficacy vaccine, vaccination is non-random and population is heterogeneous. You want to vaccinate everyone who agrees to take it. Just like with children diseases, there will be clusters of anti-vaxxers, or people just don't bother and they are often clumped together, travel around the world and spread the disease.