Vampire Yui is related to Miyu...umm let's see 
here Yui's father was a shinma, and her mother 
was a human. When her father was killed by Miyu 
her mother became friends with her, she gave Miyu 
her blood for a "happy dream". Yui, I'd assume 
from her father gets the sudden need of blood and 
Miyu comes to start her off, giving her some of 
her blood. Yui then becomes a vampire...  As far 
as I know Miyu pops in and out rarely to check in 
on Yui. ~But so far there is only ONE graphic 
novel on Yui in ENGLISH. Here's the web page 
address to get more info....

http://www.ironcat.com/titles/index.php?
series=vampireyui