That said, there are a number of steps you can take to increase your chances of survival during a (highly improbable) attack, according to Richard Peirce, a shark expert and former chairman of the UK-based Shark Trust charity.
Before you get in the water...
1. River mouths might not be the best place to swim
Peirce recommends avoiding estuaries, particularly where there are bull sharks -- which, along with great whites and tiger sharks, are the most likely to attack humans.
"An awful lot of attacks occur in river mouths, where there is silt and other material in suspension in the river -- people washing their clothes, people washing themselves," says Peirce, who has spent time in Jeffreys Bay, South Africa, where Fanning's encounter occurred Sunday.
2. Avoid fishing boats
Before you jump in the sea, have a look around the horizon -- what do you see? If you see fishing boats, Peirce says "forget it."
"If fisherman are catching fish or struggling with fish in the water, that's one of the prime attractors for a shark," he says. "So when you've hooked a fish before you've landed it on the boat, the whole time it's struggling in the water it's likely to be emitting fluids, leaking blood and acids ... all the signals that would attract a shark."
It doesn't matter the size of the fishing operation either. "Whether they're commercial or recreational fishermen, they're often discarding material -- fish they don't want, fish parts, gutting fish. They're effectively putting chum in the water and bringing around sharks."
3. Mistaken identity
Swimming early in the morning or late at night can be lovely, but it's also the time when a shark attack is most likely.
"A lot of shark attacks are cases of mistaken identity," Peirce says, "due to reduced visibility and identification ability on the behalf of the shark."
4. Don't bleed -- or pee -- in the water
Sharks have an extraordinary sense of smell and can detect a drop of blood in several hundred million parts of water, according to Peirce.
Blood indicates the presence of something to eat and may attract sharks, says Peirce, "but what's often not realized is that urine has the exact same effect. And if you're sitting on a surfboard in the water all day, you're peeing all day through your wetsuit."
Peirce also says women who are menstruating should stay on the beach -- and that people who cut themselves while swimming should get out of the water.
If you find yourself in the middle of an attack...
1. Don't panic
So you're being circled by a shark. It's not the best thing that's ever happened to you, but the worst thing you can do right now is panic.
"Don't start splashing around -- you're just going to excite, incite and encourage the shark's interest," says Peirce.
Humans, apes, dogs and cats all have paws and hands. If we want to explore something we pick it up and we touch it, we feel it, we put it to our nose.
"A shark has got no paws or hands, so if it wants to explore something, the only capability it's got to do that is to put it in its mouth," says Peirce. "That's why we often get exploratory bites which don't result in death and sometimes don't even result in serious injury. If you go swimming and splashing away, you're almost inviting the shark to come give you an exploratory or an attack bite."
2. Maintain eye contact
As the shark swims around you, keep your head on a swivel and try to maintain eye contact.
"Sharks are ambush predators," Peirce explains. "If you're turning around and facing it the whole time while it circles you, it's not going to be half as comfortable as if it's able to sneak up from behind."
3. Stay big ... or get small
This is where it gets complicated. If a shark is clearly in attack mode, you need to make yourself as big as possible in the water, according to Peirce: "The bigger you are in the water, the more respect you'll get."
But if the shark seems to simply be passing through, Peirce's advice is to roll up into a ball.
"If a shark sees you as a competitor for its food source, that can be one reason it attacks you," he explains.
"If I didn't want to be seen by a great white shark as a competitor -- and if it wasn't showing massive interest in me -- I would actually curl up so he shows even less interest in me."
4. Don't play dead
This isn't a bear, it's a shark. If you find yourself in an aggressive encounter, give it hell: punch, kick and poke at sensitive spots -- but be careful where you aim.
"There's all this talk about punching a shark in the nose. That's okay, but remember that just underneath the nose is a mouth," says Peirce. "This is a moving object in the water and you're not staying still either, so what you don't want to do is end up effectively punching at the mouth or anywhere near it."
A good shot to the gills can also do the job: "The gills are very sensitive -- giving a shark a whack in the gills isn't a bad idea."
Are you carrying anything with you? If so, turn it into a weapon. "If you're a diver with an underwater camera, use it, if you're a snorkeler, rip off your snorkel and use it to poke the shark," Peirce says.
"I've had a lot of sharks come at me, and it's (been) enough to use a shark billy -- a small metal rod between two and three feet long -- and I've just given them a little nudge on their nose."
5. Cut off the angles
If you're a diver and you run into trouble, try to get into a position where the shark can't get behind you, says Peirce.
"Keep your back to something like a coral reef. Then you've only got one direction to look. You're protected from behind, for example, and that enables you to keep the shark in sight in front of you and maybe swim to the top of the reef slowly to where your boat is."
6. Slowly back away
This goes back to the first point: displacing the least amount of water possible -- ie no thrashing and splashing around -- gradually swim backwards away from the shark towards shore.
"You must try and keep the animal in sight and very slowly and gently try and swim backwards and get into shallow water. Again, you've got to be careful -- large sharks can attack in very shallow depths."
Doing the above may help to a degree, but Peirce says the likelihood of escaping an attack from a big shark without injury is slim.
"If a white shark is in full attack mode, there's not much you're going to be able to do at that point," he says.