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Approximately 30 inmates detained in the jail’s Hermiston Hall have tested positive with coronavirus. A further 200 are isolating among.
It is understood the outbreak has not affected other areas of the establishment, which holds up to 800 remand and convicted prisoners of both sexes.
In other prisons, increased testing has been directly linked to reports of fresh cases.
A Scottish Prison Service spokesman confirmed the siutation at HMP Edinburgh.
He said: “There have been a number of cases and a group of prisoners have been isolated as a precaution.
"This is being managed in line in the same manner as with similar situations in other establishments.”