The native long-haired rat, or rattus villosissimus, normally lives in the Barkly Tableland of the Northern Territory and in western Queensland.
But now it has been spotted in Alice Springs for the first time in 25 years.
"Some of them get up to about 30cm [12in] long - fair lump of a rat," livestock manager Chris Giles said.
"They will run around and hide under a little bit of shrub there, and you can get pretty close to them," Mr Giles, a stockman on the Northern Territory's Lake Nash Station, told Australia's ABC News.
"I nearly caught one the other day."'Red Centre nomads'
Peter McDonald, acting scientist with Northern Territory Biodiversity Conservation, said the phenomenon was a "huge event" which he attributed to a run of consecutive good, high rainfall seasons.
"It is unusual in the rodent world but rattus villosissimus are unique in that way and they are pretty famous for their eruptions," he added.
"Probably the only similar expansion by a rodent is seen in the lemmings in the northern hemisphere with their eruptions. There is nothing else in Australia which erupts over such a large area."
Alice Springs generally has no rats because of its arid climate.
The long-haired rodent was first sighted around the middle of last year on the edge of the Simpson Desert, south-east of the town, Mr McDonald said.
Its ability to produce 12 babies every three weeks gives it the highest reproductive potential of any rodent in Australia, he noted.
For those anxious about a plague of rats, the scientist also pointed out that they were unlikely to stay put in the country's "Red Centre".
"It's not really ideal for them," he said. "The chances are they are just moving through and they won't set up camp or be too much of a nuisance."
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