Michael and Paula McCann and their two young children returned from a holiday to find their terraced house infested by rodents.
Wires of electrical appliances had been eaten through and faeces littered the floors of the property in Rutland Street, off Belfast’s Ormeau Road.
The couple believe the rats were able to overrun the house because they had put their cat, Lady, in a cattery while they were on holiday.
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The family are now staying with friends.
The Northern Ireland Housing Executive, which owns the property, is currently looking for alternative accommodation for them.
Pest control workers from Belfast City Council are trying to eradicate the infestation.
“I caught eight rats in the first 12 hours of having the traps down, then another four, and over 24 hours I’d caught a total of 19,” Mr McCann told the Belfast Live website.
“They were big, grey rats. The look of them was disgusting and to think they were in our home near our children was awful.”
Mrs McCann added: “We now think Lady must have been keeping the rat problem under control to a degree but the moment she went into the cattery, the rats struck.
“It’s hard to believe that in 2016 housing in Belfast could be infested by rats.
“Whatever has done it, we’ve been made homeless by a plague of rats. All we can do now is wait for the Housing Executive to help us find a new home and thankfully they seem to understand.”
A Housing Executive spokesman said: “We are aware of the issues at this property and are working closely with the family.
“Temporary accommodation was offered to the family but they opted to make their own temporary arrangements.
“We first received a report of rats in the dwelling two weeks ago when an environmental health team was engaged and we carried out repairs to the property based on their report.
“After a follow-up inspection by pest controllers yesterday, we were told rats had returned to the property.
“We received another inspection report yesterday and more work will be carried out by the Housing Executive on the property immediately.
“Our staff also met with the family again yesterday to discuss housing options, which will include a possible permanent move away from this property.”
A Belfast City Council spokesman said: “Our environmental health officers and pest control team are aware of the ongoing rat problem at the property on Rutland Street.
“We are working closely with the Housing Executive to resolve the issue to ensure that the property is made habitable again.”