Finally, in Figure 3C , we show control of an epidemic in a population of 100,000, beginning with 1000 initial infectives, keeping all other parameters the same as in Figure  3A . Each curve corresponds to the indicated number of possible ring vaccinations per day. This figure shows that assuming sufficient capacity, ring vaccination is in principle capable of containing even epidemics beginning with very many infected individuals. However, mass vaccination in such cases is justified because of the far larger number of individuals at risk and the inability to perform such extensive contact tracing.