Smallpox could be eliminated, but not influenza, because smallpox changes slowly, meaning that a vaccine can act against it in a large population over a long time. Influenza, however, changes rapidly and a new vaccine is needed every year. This happens too fast for the elimination of influenza.
Work Step by Step
This highlights the limitation on the effectiveness of the immune system presented by targets which change antigens rapidly--the immune system has a hard time keeping up.