Please tell the single word for "to completely root out a disease".
Etymology is from Eradicare. Eradicare, in turn, can be traced back to the Latin word radix, meaning "root" or "radish." Although eradicate began life as a word for literal uprooting, by the mid-17th century it had developed a metaphorical application to removing things.
Eradication is the reduction of an infectious disease's prevalence in the global host population to zero.
You just touched on a common confusion, that between 'eliminate' and 'eradicate'. They are almost identical (besides nuanced collocations and frequencies).
In the context of disease, both are used for the state where no one has a particular it anymore. But the American CDC has stipulated definitions to contrast some important situations.
They define a set of words in ever declining prevalence:
- control - prevalence has been restricted to an acceptable level
- elimination of disease - the disease does not occur _in a given restricted geological area. For example, polio has been eliminated from Canada (no one currently has the disease polio there), but there are still instances of polio in India
- elimination of infection - no one in a geographic area has shown positive tests for the organism (implying no disease and no likelihood of it starting back up again)
- eradication - no one on Earth anywhere has evidence of the organism (may exist in a lab)
- extinction - the infectious agent no longer exists on Earth at all. For example, smallpox has been eradicated (it is not out in the wild but there are some vials of it in highly secure labs).
Note that these are officially sanctioned technical uses. In informal conversation, either would be understood that 'no one gets that disease anymore and it can't come back'. But on the news or in a journal article or in science reporting eliminate refers to a particular location and eradicate refers to the whole world.
For example, the New York Times 08 April 1923 quotes ever-controversial Margaret Sanger:
Birth Control is not contraception indiscriminately and thoughtlessly practiced. It means the release and cultivation of the better racial elements in our society, and the gradual suppression, elimination and eventual extirpation of defective stocks — those human weeds which threaten the blooming of the finest flowers of American civilization.
Although eradicate is clearly the right word -- even etymologically, as it derives from radix, root -- I prefer extirpate. Although its origin in stirps, "stem", perhaps casts it as less thorough than eradication, in the words of Bender Rodriguez, "the X makes it sound cool."
Edit: a commenter informs us that in this case, the etymology is accurate: at least in technical contexts, something eradicated is removed from existence, root and branch; something extirpated merely has suffered a local stem to be pruned.
But I stand by my choice, on euphonic grounds. The "x" and then the crisp "p" make it sound even more devastating than "exterminate".