That's not how eliminating viruses works - just because there's currently some transmission doesn't mean that it's impossible to get to a point of elimination. The elimination of polio wasn't strictly dependent on quickly identifying and isolating people who were infected — obviously this is helpful and containing transmission (like what's happening here) is very important, but it's possible to eradicate a virus in a population with robust social programs supporting the effort even if there is some margin of error around false-negative test results and vaccine failure.