https://www.bbc.co.uk/news/uk-england-manchester-55992802House-to-house testing is taking place in the Fallowfield, Hulme, Moss Side and Whalley Range districts.
Father-of-one Lloyd Brown, 48, who lives in Moss Side, said: "People are worried and a bit fearful over what might happen and where this could lead. We just want all this to end."
Gary Wilson, 51, who lives in Whalley Range, said: "It's the last thing anyone wants."
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Manchester City Council has urged residents to get tested and said while the variant is more transmissible there is no reason to be concerned it is any more severe than others.
The authority said those people without symptoms could get tested at Our Lady's Presbytery on Raby Street or Guru Nanak Dev Ji Gurdwara on Monton Street.