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Mumps has broken out among staff at Gillingham's new Tesco Extra store.
Ten people have been off work from the Courteney Road store suffering from an illness with mumps-like symptoms in the last month.
A spokesman said: "It is under control and everyone is receiving medication. Over more than 500 people work at the store so it is a very small percentage.
"Where staff have felt ill at the store they have been sent home immediately. If anyone has phoned in with the symptoms, they have been told to stay at home for seven days."
The store reopened at the end of February after an extensive refurbishment and expansion.
A member of the public contacted the Medway Messenger to express her concern about mumps there because she has family members who use the store with young children, some of whom had not had their MMR vaccinations.
The outbreak matches a recent sharp rise in the number of cases of measles and mumps nationally and across Kent.
The general situation has prompted the Health Protection Agency (HPA) in the south east to reiterate a warning to parents, urging them to ensure children are fully protected with two doses of MMR vaccine.
Spokesman Teresa Cash said: "We have not been made aware of a particular problem/outbreak in Gillingham. There has been an increase in reports of mumps-like symptoms in the Kent HPU area over the last few days.
"These are as yet unconfirmed by laboratory testing. These reports are of individual cases - some of whom may well have connections to particular places but this is a detail about which we would not necessarily always be informed."
So far in 2011 in the Kent Health Protection Unit (HPU) there have been 115 reports of mumps-like symptoms, but only 24 confirmed cases.
There were 52 confirmed cases in the same period in 2010. In the whole of 2010, the Kent HPU had 116 confirmed cases of mumps.
Data had been recorded differently in previous years so it was not possible to give a proper comparison.
Ms Cash added: "It should be noted that it is likely that many cases go undiagnosed or unreported."
From January to the end of March 2011, there had been 19 confirmed cases of measles in Kent, one of the highest levels in the south east region with a total of 42 for the period.
In the whole of 2010 in Kent, there were seven confirmed cases of measles with 107 confirmed cases in 2009.