This would not be possible. There are at least several species of animals (mikes, civets, and bats) than can transmit this virus. We would need to quarantine and test, or kill, each and every one of these animals to be sure we eliminate this virus, or else it will eventually make its way back to humans.
My opinion, based on what I read, is that this will be a bit of a scourge until such time as enough people have immunity from either catching it or getting vaccinated.
Over time, as this new coronavirus makes its way through the human population, the experts it to become less virulent in general and/or appear less often. [0]
[0] https://www.statnews.com/2020/02/04/two-scenarios-if-new-cor...
https://www.cdc.gov/coronavirus/2019-ncov/daily-life-coping/...
Agree with the main thrust of the point but if everyone did stay home for 14 days you may well eradicate the virus. Problem of course that its economically/socially/medically impossible to facilitate a complete 14 day lockdown.