I'll be honest. I don't see anything remarkable about the map, apart from the ancient ruin revealing camps that far away. A couple of those camps are pretty far from you. The spacing between the camps looks like normal spacing to me.
If it's Prince difficulty, then you should have a 40% bonus against barbs. And if it's not raging barbs, they won't spawn from the camps too quickly. Although when you clear one camp, another will immediately spawn somewhere else, that's my understanding of how barbarians work. It seems to me like the game tries to maintain both a minimum number of barb encampments in the world.
If you're really having so much trouble with the barbs, then get the Honor opener and go wild. Give up on wonderspamming and build units instead. And lessen the amount of territory for them to spawn in. Send escorted settlers out to found new cities. Cities can defend themselves; there is no way one, two, or even three barbs will be able to capture a city.
Defending trade routes and tile improvements could be a bit harder though. You should have units defending your cities and workers for that. Trade routes that pass through the fog of war are vulnerable; units can help light the place up.
