Earlier quoted context omitted.
The latest data (preprint, not peer reviewed etc etc) mention memory B and T cells up to 8 months after recovery from the illness. This means that an immunity of one year is probably likely. This would be probably enough to quench the spread, but not to eradicate the virus.
I think we can eradicate it by contact tracing. With 90% efficiency it will be extremely tough for the virus to spread. For any new cases you simply test everyone in the vicinity of the infected person. But I don't think even that will be necessary. 90% efficiency reduces R so much, it will probably die out on its own. The real problem is mutations that are not covered by the vaccine. If it mutates as efficiently as…
We will get vaccines and we will come up with better treatments negating its effects, but this coronavirus is here to stay. It will be a fifth endemic human coronavirus.