Stabbed girl's body doused in acid
Yousef, an asylum seeker from Somalia, was initially charged with Alia's murder but after psychiatric assessment she was ruled unfit to plead to the charge and jurors at Birmingham Crown Court were instructed to consider whether she committed the act of unlawfully killing her daughter.
The child's body was discovered by police officers who forced entry to Yousef's home in Milverton Road on February 13.
The court heard the child had been stabbed repeatedly and acid had corroded her skin, bones and internal organs.
Mr Justice Flaux, sentencing, said: "This is a terrible and tragic case. The defendant, Iman Omar Yousef, who is now 25, suffers from a serious mental illness, paranoid schizophrenia.
"On the night of February 12 this year she killed her daughter Alia in a frenzied attack with a knife or similar sharp weapon and then poured a corrosive agent ... possibly sulphuric acid over the body after the child was dead, possibly in an effort to dispose of the body.
"She (Yousef) had clearly been mentally ill for some time and it was while in the grip of that derangement that she committed that awful act.
"She continues to pose a risk both to herself and to the public at large.
"I am quite satisfied that it is necessary for the protection of the public from serious harm for this lady to be detained in hospital."
The court heard Yousef had been suffering from delusional thinking and hallucinations for a two year period before killing her daughter.
During the trial it emerged that Yousef's mother and aunt, who lived in Leicester, had concerns for her mental health soon after she arrived in the UK in 2007, describing her as "acting strangely and talking to herself".
Her mother told police she had removed large knives from her daughter's possession on two occasions and described her as "confused and irrational".
A housing officer referred the case to social services 10 days before Alia was found dead, and a visit was made to Yousef's home on February 12.
A spokesman for the Birmingham Safeguarding Children Board said a serious case review had been initiated and would now be sent to Ofsted. A spokesman said: "We cannot comment any further at this stage."
Detective Chief Inspector Tim Bacon, of West Midlands Police, said Yousef made six 999 calls on February 12 claiming there were people outside her home trying to get in.
He said Yousef was convinced there were people from Leicester "after her" and told officers she was frightened and did not feel safe at the rented property.
Mr Bacon said two officers spent around an hour an a half at the address and found no evidence of anyone outside.
He added: "I am certain that there were no people from Leicester or otherwise who were putting Mrs Yousef in this fear.
"Certainly there is absolutely no evidence whatsoever that there were any such people and indeed, other than making references to people from Leicester, she could never be specific about who those individuals were."
The same two police officers were sent to Yousef's rented home the following day, where they discovered Alia's body, partly covered with bin liners on a bedroom floor.