MARSHAL,
EDISONForlornIsland
A yachting party is shipwrecked on a remote
AleutianIsland
, forcing the castaways to struggle for survival and order, among themselves and the hardscabble natives. Published hardcover in 1932 and paperback in 1949.
I don't know any more about this book and I don't know how old the book is that you were reading. I don't know if the natives were sick with incurable diseases.