Looking for

I'm looking for this manga where in the world there is a disease where people age younger and aventually disappear.the main focus is about a girl and her sister who has the illness the girl is living with a man who said he is their cousin and is researching the illness. A man comes along who use to be with the girls mother he is a demon and their mother was his chain. The main girl is also a chain and tames a demon and makes him look like a famous model.

Sorry wasn't quite sure how best to describe it. I can't remember the name and really want to read the rest, does anyone know the name?? X