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Three of those children are pupils at Cadle Primary School, where parents have been kept informed of the infection through letters sent home, and vaccinations have been offered to relatives.
Public Health Wales say investigations are still on-going into the outbreak, which can be prevented by vaccination, good hygiene and sanitation.
And in the meantime pupils there have stuck up for they describe as a "fantastic" school.
Ihsan Miah, aged 10, said: "Cadle is clean, we are not dirty.
"We have fabulous cleaners, they clean the building top to bottom.
"They stay in the school until late working like mad. The school is so clean and shiny it gleams.
Casey Lee Ward, aged 9, said: "We sterilise water bottles every week with chlorine, and we wash our hands after the toilet, and before breakfast club and before dinner. Please don't blame us for the germs, we are not a dirty school — our school is fantastic".
The letter sent home with pupils told parents the source of the infection was from outside the school, and asked for their co-operation.
Teacher Liz Tucker said: "We have been talking with pupils about what is going on, and getting the children to discuss the issue. They went back to class, and they decided they wanted people to know that Cadle is a nice school.
"They wrote a letter which they sent to the Evening Post, inviting them to come and see the school for themselves.
"We are very proud of them."
Dr Jörg Hoffmann, consultant in communicable disease control, Public Health Wales, said: "Investigations are under way to determine the source of the infection and close family contacts of the children are being offered hepatitis A vaccination as a precautionary measure.
"There is no evidence at present that the infection has been transmitted within the school or that there is any wider public risk to the community.
"We are working closely with Swansea Council environmental health officers to investigate the cases and to offer advice to parents, school staff and pupils."