So far, outbreaks have occurred in areas with exceptionally high biodiversity.
Now, Hayman and a team of international researchers have developed a model to identify potential carriers of filoviruses using an algorithm that analyses traits of filovirus-positive bat species to identify hotspots where those species co-occur.
This profile was built using the life history, physiological, and ecological attributes of the 21 bat species known to harbour filoviruses.
With 57 variables, from diet and reproductive behaviour to migratory patterns and species density, the algorithm predicted features that distinguished bats that had tested positive for filoviruses from other bat species with 87 per cent accuracy.
When the world's bat species were compared against this profile, many new potential bat hosts were identified based on their traits.
While many are found in sub-Saharan Africa, they were more widely distributed than the team expected, ranging across Southeast Asia and Central and South America.
Hayman, who authored the only studies to show evidence of Ebola virus in West African bats, said the model allowed researchers to find patterns in the data that only a machine could identify.
"Instead of looking at a map and predicting where outbreaks will occur in relation to previous outbreaks, it looks at the map and predicts outbreaks where the identified species are found.
"The Ebola virus may have faded from the public eye, but the conditions, animals and viruses are still present around the world and there is still a great need to maintain surveillance and research."
But there was nothing to suggest Kiwis might be at any extra risk, he said.
My visit to a biosafety lab
When visiting the most secure laboratory in Australasia, you'd expect to feel safe.
It's hard to be comfortable, however, when you're standing mere metres from a room in which the most deadly diseases in the planet - think Ebola - go under the microscope.
In New Zealand, there are a handful of "PC3" facilities, or those isolated enough to have a physical containment biosafety level of three.
These are immensely contained, built to global standards and subject to the strictest biosafety precautions.
But they're still rated below the PC4 lab I visited at Melbourne's Peter Doherty Institute for Infection and Immunity, where some of the diseases tested are terrifying just to think about.
If Ebola came to Australasia, it would be analysed here.
Of course, I wasn't shown inside the actual lab, but could view it through a thick window.
I did get to see the white rubbery suits which staff climb into before they pass through a chain of air-locked containment chambers.
The suits protect them from pathogens present when the virus is deactivated so it can be safely tested in the lab.
Inside, they hook up to a yellow air cord that allows them to breathe.
Leaving the lab involves passing back through each of the chambers, doused with chemicals that kill any lingering viruses.
The lab itself is decontaminated with chemical bombs or a good blast of gamma radiation.
While all of this should have more than reassured me, I still felt much more comfortable when I was out of there.