I’m writing a novel set on a solitary island.
An orphan island is one that's all alone, without any other island friends or family. That's what makes it a solitary island.
This is a jukugo word that uses the on'yomi readings of the kanji. You didn't learn this reading for 島 yet, so here's a mnemonic to help you:
There are a few solitary islands off the coast of Japan that are actually considered to be a part of Tokyo (とう). Usually people think Tokyo is just the big city on the mainland, but it includes these little, lonely islands too!