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The 67-year-old is serving a whole life sentence for the murders of 10 women and girls at HMP New Hall.
West was given the jab last week, The Sun reports.
Prisoners are being vaccinated in the same priority order as everyone else - and West is in the 'extremely vulnerable' group, meaning she's eligible for the vaccine.
The Ministry of Justice told LADbible: "Prisoners are being vaccinated at the same time as the general public and in line with the priority groups set out by the independent Joint Committee on Vaccination and Immunisation."
A source told The Sun that West had a 'bad reaction' to the jab and was left feeling unwell.
They said: "She suffered quite a bad reaction. There were lots of flu-like symptoms and she took to her bed."
Another source told the news outlet: "Rose is hugely overweight, getting older and has been locked up for years.
"Her health isn't great and she's undoubtedly at greater risk of Covid than many on the outside.
"But does that really mean she should be the first in the queue?"
Last week it was revealed that 76-year-old sex offender Gary Glitter, real name Paul Gadd, had been given the jab.
Being 76, he is in the high-risk category and, in line with the rules, was eligible for the vaccine.
But not everyone was happy with the news and some questioned why he was being vaccinated while others were still waiting.
David Spencer, Director of the Centre For Crime Prevention, told The Sun: "There are plenty of key workers and vulnerable people still to receive their jab.
"It is wrong to single out criminals ahead of them. This decision needs an urgent rethink."
However, former Chief Crown Prosecutor Nazir Afzal was one of those who spoke in defence of vaccinating prisoners as it helps to keep prison staff, who are key workers, safe as well as the wider prison population.
He tweeted: "Gary Glitter went to prison on my watch thanks to a brilliant police/prosecution team.
"It's okay that he has been given a Covid vaccine because it protects everyone in that prison, the staff, their families & other prisoners inc those on remand who are innocent till proven guilty."
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