As others have suggested, a couple centuries is the ball-bark estimate.
There is an effect that would probably be very strong. That would be loss of some local cultural groups, and changes in cultural patterns. This was also observed in many other places that have had severe epidemics.
What happens is this. There is a local culture, say a group that shares a language, a religion, a farming process, a hunter-gatherer culture, etc. Think of the various groups of natives in the great plains. Or the folks in the very far north who had a combined ocean-ice and land-based lifestyle.
Then the epidemic comes through and removes a significant fraction of them. And this has the effect that many critical skills are removed. The people who know how to do some critical skill all die, or enough of them die that the culture cannot maintain continuity.
So they lose some critical skills. The guy in the far north who knows how to make those great kayaks. Or the guy in the great plains who can read the weather and tell you when to plant corn. Or the story teller of the group, so that all those great lessons are lost. And so on.
So losing even as few as 10% of the population has caused local villages to collapse and become uninhabitable. And when a significant number of villages are lost, then trade routes and cultural contact can collapse with them. And entire cultures can collapse. Or, if it is not too extreme, fragment and withdraw from wide areas.
So the result is, cultures that were previously stable with one pattern, will emerge drastically changed. The pattern is Europe after the Black Death. Social patterns that existed for centuries were radically weakened and, shortly thereafter, radically changed.
The changes are very difficult to predict since it depends exactly where the worst effects fall. In Europe, one effect was that the nobility was significantly weakened relative to commoners. Thus various political and cultural processes that we are still feeling the effects of were strongly moved forward.
So the numbers may recover in a century or two. But the social effects may be quite drastic and discernable basically permanently.