Johnny Deppin tytär voi jo paremmin!

Johnny Depp' s daughter, who has reportedly fallen ill in England, is " doing much better" the actor' s rep said in a statement Thursday.



" We are happy to report that their daughter is doing much better," Depp' s rep, Robin Baum, said in a statement. " The family greatly appreciates the continued support and respect of their privacy."



Depp and his longtime girlfriend , Vanessa Paradis, have two children, Lily-Rose, 7, and Jack, 5.



Several British papers have reported that Lily-Rose came down with an undisclosed illness over a week ago and that Depp, 43, has been by her bedside every day.



Depp has been filming a movie version of the stage musical Sweeney Todd for DreamWorks. A studio rep tells PEOPLE: " We have adjusted the schedule to accommodate [Depp' s] needs at this moment. We understand that [Lily-Rose] is improving. ... Obviously everybody at the studio is certainly with them in their good spirits."