After feeding on a host's flesh, the maggots will typically exit the body via wounds they have created on the skin. They will then become bot flies.
Extraction takes place by placing Vaseline - or a similar substance - on the wounds. After the maggots have been suffocated, they can be extracted with tweezers.
Dr Marc Shaw, from Auckland's Worldwise Travellers Health and Vaccination Centre, said the infection was not uncommon amongst New Zealanders.
"I've probably extracted them from about five or six people over the past few years.
"It's not a relatively uncommon event."
He stressed the infection was not as dramatic as it sounded.
"There's a great mythology about the bot fly, but really you just pull them out and forget about it.
"They're quite robust little blighters, but they come out relatively easily."
He also said that it would be impossible for those who suffer from the infection to spread it to other New Zealanders, with our relatively cool climate making it near-impossible.
"There's no history of that in our climate. We just don't have the conditions."
He recommended those travelling to either South America or Africa take particular care on beaches, where people were most likely to be infected.
Because the flies often attach their eggs to mosquitos, who then bite a host and leave then with the infection, he said insect repellent is a must.
Long pants, proper footwear, and light-coloured clothing can also help protect travellers from the bot fly.
Vaag and Williams will remain in Bolivia until at least next month, by which time they should be fully healed.