Kingston Crescent Surgery, in North End, has closed early due to a suspected case of the disease, which has infected more than 65,000 people and killed more than 1,300 worldwide.
Maxine Ryan, a hairdresser from North End, said she was concerned about the spread of the illness – which poses a serious health risk to already unwell, elderly, or young people – as she is the mother of a five-year-old girl.
The 31-year-old said: ‘I worry about her getting it.
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‘I want more information – I have felt a bit left int he dark about it.’
A patient at the surgery said she hoped staff would release more information.
Janet Sparks, 63, from North End, said: ‘I think they should let people know what's going on. Especially if they are patients here.
‘If there is a case here, I wouldn't be worried - I’ve not been in contact with anyone who has been abroad.’
The surgery posted a warning on its website to let visitors know it was closed due to a suspected case of coronavirus, official named Covid-19.
One Southsea resident feels the UK is ‘better able to deal’ with the disease than its country of origin, China, which has recorded 5,000 more cases within the last 24 hours.
Marieke Ruttegers said: ‘I would worried if it came here, but I think we are better able to deal with it than in China.’
But not everyone is worried, with Nicole Mitchell, from Buckland, left ‘not bothered’ by the announcement.’
She said: ‘I'm not bothered. First it was Ebola, now this. It will die down.’