Theoretically, the infection COULD be eradicated completely.
If everybody was shut up in a defined space for a certain time (two weeks?) with absolutely no human contact, the coronavirus would have no host. Borders would have to be totally locked down too.
Of course, that would be totally unacceptable. The people who are already infected and those with illnesses requiring medical care would die. A few young children, old and disabled people would die too.
When formulating a plan, the government should concentrate only on the essential contact needed to make sure that those who can't be self-sufficient don't die.