Ooh, sounds awful, thank heavens we don't have those over here. I've got no solutions for you I'm afraid.

Ouch!...And ooh, ouch, and wouch!! Definitely a disaster! Have you tried some of the things that have worked in the USA?

Baits with spinosad--if that's legal in South Africa.

A pound of fresh spearmint, a cup of cheap olive oil, a cup of water, and 1/4 cup of organic dish soap. Liquify it thoroughly in a blender, and strain it. Then mix 2 ounces per gallon of water, and spray about one gallon per 300 square feet, once a month.

A similar mix, but with orange or tangerine peel, instead of the mint.

I hope one of these works, but the ----- keep finding ways to get around controls!!

Check out wikipedia for info on control ... "Due to their nesting behavior and presence of numerous queens in each colony, it is generally impractical to spray Argentine ants with pesticides or to use boiling water as with mound building ants. Spraying with pesticides has occasionally stimulated increased egg-laying by the queens, compounding the problem.[12] Pest control usually requires exploiting their omnivorous dietary habits, through use of slow-acting poison bait, which will be carried back to the nest by the workers, eventually killing all the individuals, including the queens. It may take four to five days to eradicate a colony in this manner. Researchers from the University of California, Irvine, have developed a way to use the scent of Argentine ants against them.[13] The exoskeletons of the ants are covered with a hydrocarbon-laced secretion. They made a compound that is different, but similar, to the one that coats the ants. If the chemical is applied to an ant, the other members of the colony will kill it.[14] The chemical method may be effective in combination with other methods."

Naturally, the victims [humans] of these nasty ants have tried all sorts of means to get them out of this town, but NOTHING works effectively.
This is a REAL INVASION and a terrifying plague never before experienced around the world to the days of Pharaohs!
I use Blue Death Multi Insect Powder made by Doom, and have wasted kilograms of this poisonous powder to no avail.
Boiling water works for a few hours... but they seem to multiply at an impossible to stop rate!
Middle of Summer - now in the Southern Hemisphere - they invade everywhere.
There are billions, even trillions around the suburb where I live.
If my granddaughter leaves a crumb of bread on the carpet, it takes a few minutes to see a safari of ants marching towards it!

Unfortunately, judging by the active ingredients, Blue Death would be one of the least effective products that you could use. I would look for baits containing spinosad--which is semi-organic--or hydramethylnon--which is more toxic.

Another simpler thought my quote from wikipedia above did not cover ... have you tried applying a thick layer of common table salt around the boundaries of your house? East african safari ants avoided this totally - didn't kill them just displaced them in-situ and diverted their route. I shall never forget waking up one morning to discover a whole army moving through my bedroom - I hollered and yelled until someone came with a bucket of salt so I could get out of bed!! If you can find the nest - fire it.

Wish to report that my son found a product that seems to be quite efficient in destroying Argentine ants.
It is called Maxforce Ant, by Bayer.
Expensive.
I've used it now for a few weeks and it has killed thousands of ants around the house.
The ants go straight away to the granules and carry them inside the holes.
A week later, you see them throwing out the thousands of dead one.
Let us hope this will reduce the pestering population around this house, since it is impossible to destroy the whole monstrous colony around the city.

http://www.bayerhome.co.za/index.php?option=3&id=1&com_id=104&parent_id=86&com_task=1

That has the second active ingredient that I mentioned--though I didn't know that Bayer had a product with it. I've often used Amdro.