10/16/2012 AT 07:50 AM EDT
Doctors tending to Malala Yousafzai, the Pakistani 15-year-old who was shot in the head
by the Taliban last week, say she could make a "good recovery" – although concerns for her security have arisen as intruders have attempted to enter the British hospital where she is being treated.
"We have had some ... irritating incidents overnight, and I understand that a number of people have been arrested but there are no security concerns," Queen Elizabeth Hospital medical director David Rosser told reporters on Tuesday.
"I understand that a number of people turned up claiming to be members of Malala's family – which we don't believe to be true – and have been arrested," he added.
Every attempt to reach Malala has been averted by police, who also say that, despite Rosser's remarks, "No arrests were made, and at no point was there any threat to Malala." Any well-wisher hoping to see her has been stopped at the gate and questioned, say West Midlands Police.
On Tuesday, a week after two gunmen intercepted her school bus in the former Taliban stronghold of the Swat valley because she had expressed the opinion that girls should go to school, Malala was spending her first full day in the U.K. She had been flown into Birmingham Airport on an air ambulance on Monday, before being taken to the Queen Elizabeth Hospital.
Regarding her condition, Rosser said Tuesday that doctors believed she had "a chance of making a good recovery."
"Clearly," he said, "it would be inappropriate on every level, not least for her, to put her through all of this if there was no hope of decent recovery."
He continued, "We are very pleased with the progress she has made so far. She is showing every sign of being just as every bit as strong as we've been led to believe she is."
Rosser also said that the schoolgirl will need "reconstructive surgery" as part of her prolonged care.
Messages of support and offers of financial assistance for Malala have flooded the hospital. Those wishing to donate may click here
Additional reporting by SIMON PERRY