It was the final straw and she broke off the relationship.
Her mother, Tsehaynesh Medhani, called in the police, but Arsema was unwilling to file a formal complaint.
Ms Medhani feared for her daughter and tried to ensure she was escorted home from school every day.
But Nugusse told Arsema's mother: "How many days are you going to accompany her? I'll kill her one day."
He kept his word on 2 June 2008.
An Old Bailey jury was shown CCTV footage of Nugusse following her into the block of flats near Waterloo station where she lived.
Arsema Dawit had chosen not to pursue a complaint against Nugusse
She was stabbed more than 30 times, mainly in the neck, and her body was found 20 minutes later by a neighbour, returning home after picking up her eight-year-old daughter from school.
Nugusse, a 22-year-old civil engineering student, from Ilford, Essex, walked to nearby Hungerford Bridge and made a 999 call.
He immediately confessed to what he had done, but tellingly he appeared unaware Arsema had ended their relationship and continued to refer to her as "my girlfriend".
He threatened to jump into the River Thames. For 35 minutes the operator kept him on the phone, until police officers finally located and arrested him.
Two weeks later Nugusse tried to hang himself in his cell. He was cut free but had suffered severe brain damage.
Unable to communicate with his lawyers, he was declared unfit for trial. Judge Peter Beaumont said it would be a "heartless act" to make him attend court.
So this week a jury at the Old Bailey was shown the overwhelming evidence against him and, after a brief "trial of issue", decided he was responsible for Arsema's death.
He was ordered to be detained indefinitely under a hospital order in secure conditions.
Doctors are pessimistic about him ever regaining his mental faculties.
The case, which follows the deaths in similar circumstances of Clare Bernal, Tania Moore and Rana Faruqui, highlights the police's continuing inability to protect female victims of male violence.
The teenager's body was found in the lift by a neighbour
The Independent Police Complaints Commission said that, now the criminal trial was over, it would be continuing its investigation into the allegations that the original assault had not been treated seriously enough.
Mrs Medhani said she awaited the outcome of the investigation and added "I believe Arsema's life could have been saved if the police had taken action when I approached them".
She also said: "My body is alive but my spirit is dead and I feel with her death I died too.
"It would have been better if the murderer had taken all our lives, not just Arsema's, as we have not been able to live our lives since that terrible day."
Paul Infield, a barrister and author of The Law of Harassment and Stalking, told BBC News: "The problem for the police and the CPS is how to know which of the approximately 880,000 stalking cases each year are going to become murders.
"Risk assessment is probably the best way of making that distinction. For the ordinary copper on the ground, how does he know which ones to investigate and which ones to ignore?"
Mr Infield said: "If you locked up every budding Lothario who had phoned up a girl too many times the jails would be full. But 80% of stalkers are men and a lot of those do become dangerously obsessed, and it can be very scary, especially for young women."
He said research in Britain, Australia and the US suggested that a warning or a caution from a police officer tended to stop stalking but only "if it happens before the obsessive behaviour becomes ingrained".
Mr Infield said it was understandable that a 15-year-old girl might not want to press charges and she clearly never foresaw what would happen.
It is very difficult to stop somebody like this because they will deny and minimise their actions
Dr Lorraine Sheridan
Dr Lorraine Sheridan, a psychologist and expert on stalking from Heriot-Watt University in Edinburgh, said: "Most of the dangerous stalkers are not mentally ill and do not suffer from conditions like schizophrenia. They simply have an inability to cope with rejection.
"They feel the victim is controlling them because they can't get her out of their heads and sometimes they feel the only way out of the pain is to kill them. They will often then try to kill themselves."
She said she knew of some stalking cases that had lasted 40 years.
Dr Sheridan has been working with the Association of Chief Police Officers on new risk assessment protocols about to be rolled out across the country.
Clare Bernal was shot dead by an ex-boyfriend in Harvey Nichols in London
She said police forces were getting much better in the way they dealt with stalking cases but added: "Part of the problem is that it is very difficult to stop somebody like this because they will deny and minimise their actions.
"They will often believe the victim deserves it and deny they have a problem."
The CRT (Clare, Rana and Tania) Trust was set up to campaign for more action on stalkers.
One of its members, Tracey Morgan, said: "Stalking/harassment is not a minor crime.
"This must be dealt with as murder prevention so that background checks and assessments on the alleged perpetrators are to hand and they are not released on bail or given sentences that will effectively put victims more at risk, resulting in inadequate or no protection.
"This country needs a sea change in attitude so that the human rights and life of a victim is put above that of the perpetrator."
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