Yes each week you start over with a empty island and 10 gold. Its on page 10 of the rulebook.
They call them campaigns I think weeks would have been a better term for the rounds in the game.
Thank you. Somehow, I missed page 10 in my review of the rules earlier. I was looking at page 9 thinking that not only was it the last page, but the most sensible place for them to address all of that.