Some infections can be eradicated from the face of the planet. Smallpox is the one example of disease eradication to date. Smallpox still exists in US and Russian labs, but there has been no wild cases since 1977. It is, like the Dorothy, history.
Why were we able to eradicate smallpox? Three reasons:
1) There is only one form of smallpox. Unlike influenza that changes from year to year. So only one vaccine needed.
2) By what appears to be a once in a universe miracle, every county cooperated with the WHO (much like we all cooperate with the IRS) so the entire planet received the vaccine. Once enough people were vaccinated, the disease was unable to perpetuate itself and spread and so died out.
3) Unlike bacteria, there are no asymptomatic smallpox carrier states. Eradicable viruses usually cause symptomatic disease and do not result in asymptomatic, infectious carrier states that serve as a reservoir for infecting others. HIV and Herpes cause chronic asymptomatic infections and will probably never be eradicated.
There are other diseases that are theoretically eradicable, like measles and polio. They have one antigenic type, have no carrier state and, if the entire world could be vaccinated, the disease would cease to exist in the wild. I am sure there would be biologic weapons labs that would always carry a vial or 2 of every infection. Just to be safe.