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Relatives of prisoners serving time in the county's jails have been told to stay away if they have coronavirus symptoms.
The minister in charge of prisons, Lucy Frazer, said governors have "well-developed policies and procedures" to deal with infectious diseases.
The seven prisons in Kent are Elmley, Standford Hill and Swaleside on Sheppey, Cookham Wood and HMP Rochester in Medway, East Sutton Park and HMP Maidstone in Maidstone.
The minister said: "We understand prisoners and their loved ones might be concerned about the situation.
"But we can assure them that we will continue to operate normal regimes, with the minimum disruption, for as long as we can.
"This will include visits to prisoners but, in line with Public Health [England] advice for the general public, we urge any friend or family member[s] not to come to a prison for a visit if they have symptoms associated with COVID-19 – a fever or new, persistent cough.
"We are also looking into ways to keep prisoners in close contact with their families in all eventualities and will share further information as and when necessary."
But the minister warned people who have a fever or new and persistent cough to stay away.
She also acknowledged prison staff may need to self-isolate if they become infected, adding steps were being taken to boost staff availability.
A Ministry of Justice spokesman refused to be drawn on whether visits would be restricted in the future, based on the potential spread of coronavirus, saying: "We aren’t going to go any further than the minister’s comments."
Hand washing facilities are available for prisoners in their cells as well as in shared areas including education blocks and kitchens.
Staff and visitors will also have access to soap and water and signs are being put up around jails encouraging people to wash their hands, she added.
Prisons are also able to isolate inmates, where necessary, if cases appear or are suspected.