Imagine the size of a common garden snail. Now multiply it several times.

Now you get an idea of the size of giant African land snails. They can grow to the size of a rat and are an extremely destructive pest, eating anything green in their wake.

That's why they are considered among the worst invasive species in the world.

Though originally from east Africa, researchers discovered that last summer that they have now reached Havana in Cuba, a finding they outline in a new report in Molluscan Research

That's an issue, not only for Cuba's plants, but for Cuban snails.

Most of Cuba's molluscs don't exist anywhere else in the world. They are also extremely diverse, but are now at risk of being outcompeted for resources by the new invaders.

Once they infiltrate the giant snails can spread quickly. They are hermaphrodites and can begin reproducing at six months. One snail can lay 100-300 eggs per month.

"The probability of these eggs hatching is 95% so the species could eventually cover the whole island," explains Antonio Vazquez of the Institute of Tropical Medicine in Havana, Cuba. He is currently monitoring just how serious the infiltration is.

The researchers do not know when they first invaded or how they got there. But they expect their numbers to increase, as they are extremely good at adapting to new ecosystems.

Cuba is not the only place the giant snails have invaded: they have also reached Brazil, Florida and Venezuela.

It will be hard to get rid of the giant snails, as molluscicide could damage the indigenous population.

Introducing another predatory snail might seem like another option but this was done in 1821 in the Hawaiian islands with some unfortunate consequences. Instead of eating the African giants, they only ate other, native snails. The African giants, it seems, were untouchable.

So what should Cuba do?

Eradication is too much to hope for, says Vazquez. Instead he wants the country to control the snails' population, to stop them spreading too far.

He hopes Cuba's mollusc surveillance programme will help monitor their population, and remove individual snails by hand.

But it will be crucial to advise the public not to collect the snails as pets. They can also pose a threat to human health as they host the rat lungworm parasite, which can cause a form of meningitis.

Follow Melissa Hogenboom and BBC Earth on twitter