The deadly coronavirus that emerged last year does not currently appear to be infectious enough to pose a global threat, researchers say.
Their analysis of 55 cases of Middle East respiratory-syndrome coronavirus, published in the Lancet, indicated the virus struggled to spread in people.
But the virus may be mutating, which means it could become a much greater threat.
It is similar to viruses that cause Sars and the common cold.
So far there have been 77 confirmed cases and 41 deaths. Most infections come from an unidentified animal source, but there have been cases in which the virus has spread between people.
On Friday it was revealed that the World Health Organization has convened a telephone conference of its International Health Relations Emergency Committee next week.
The committee has only met once before ,during the 2009 H1N1 flu outbreak.
It said the meeting was a proactive approach, rather than a sign the situation was escalating.
The team at the Pasteur Institute in Paris tried to calculate the average number of people each infected person passed the virus on to - what is known as a "basic reproduction value".
A high value means the number of cases can increase rapidly and potentially spread around the world, but a number less than one would mean the virus was destined to fade away.
The study indicated each patient would, on average, infect 0.69 others. So three infected patients would pass the virus on to just two people.
Prof Arnaud Fontanet told the BBC: "The virus as it currently stands is not able to start an epidemic.
"My concern is that people read this and not worry about it, but the opposite is true. This is the perfect time to identify the animal host and stop it."
In the early stages of Sars in late 2002 it had a basic reproduction value of 0.8, but eventually the virus mutated and could spread more easily.
"Sars' adaption to humans took just several months, whereas Middle East respiratory syndrome coronavirus has already been circulating more than a year in human populations without mutating into a pandemic form," Prof Arnaud Fontanet added.
There have been cases in Jordan, Qatar, Saudi Arabia and the United Arab Emirates. Additional cases in France, Germany, Italy, Tunisia and the UK were linked to travel to the Middle East.
On Thursday, the death of a patient in the UK was announced. He had been treated for kidney failure and severe breathing difficulties since being flown in from Qatar in September.
Dr Benjamin Neuman, from the University of Reading, said: "The authors have done their best to predict how Middle East respiratory syndrome will spread based on the few cases that we know about, and found that the virus appears to be slowly dying out.
"But other work has shown that the virus is changing, and that change makes it difficult to predict the future of Middle East respiratory syndrome.
"What most concerns me is that people are still becoming infected from an unknown source."