Don't think y our 1-1/R0 rate makes sense (I assume Re is equivalent to R0 - I'm not familiar with Re). At an R0 of 1, each person spreads to one other person. So everyone would eventually be infected, just at a linear rate. Your formula though gives 1-1/1 = 0. Similarly for an R0 less than 1 your formula goes negative.

Anyway, if R0 can be brought below 1, it wouldn't need to be indefinite. The further below 1 it is, the faster the virus will extinguish itself. This was seen in China, where they went from exponential growth to fewer new cases each day and ultimately to the situation now where most new cases are imported from other countries.

You also don't need global coordination, although it helps. Any individual country can restrict outside travel from outbreak areas, get their own R0 below 1 via social distancing to eliminate the local outbreak, and then relax social distancing locally, relying on travel restrictions and temporary quarantines of travelers from outbreak areas, plus testing and contact tracing. If cases start to flare up again, increased social distancing measures can be brought in to get them back under control.

So in theory you could do extreme distancing for a period on the order of a few months, and then normalize somewhat. It would take a global response of that sort (unlikely), a vaccine, or a change in the virus itself though to end the situation entirely.