The Zika epidemic in Latin America could be over within three years, say scientists.
Experts believe the virus, linked to a serious birth defect, is set to burn itself out as more people become immune to it.
The less welcome news is that right now the epidemic cannot be contained with existing control measures, the same team has concluded.
Professor Neil Ferguson, from the School of Public Health at Imperial College London, said: "This study uses all available data to provide an understanding of how the disease will unfold - and allows us to gauge the threat in the imminent future.
"Our analysis suggests that Zika spread is not containable, but that the epidemic will burn itself out within two to three years."
Ultimately, Zika will be the victim of its own success, say the scientists.
Thanks to our immune systems, the mosquito-spread virus is unable to infect the same person twice. In the end, a stage will be reached where there are too few people left to infect for the epidemic to continue. The phenomenon is known as "herd immunity".
After the current Zika threat has passed, another large-scale epidemic is unlikely to emerge for at least 10 years, according to the predictive modelling study published in the journal Science.
Prof Ferguson added that efforts to slow the spread of the virus may backfire by prolonging the epidemic.
"Slowing transmission between people means the population will take longer to reach the level of herd immunity needed for transmission to stop," he said. "It might also mean that the window between epidemics - which we predict may be over a decade - could actually get shorter."
Zika, carried by the Aedes aegypti mosquito, is associated with a birth defect called microcephaly which causes babies to be born with abnormally small heads and brain damage.
Fear of the virus has led a number of competitors to opt out of this year's Olympic Games in Brazil, including top British golfer Rory McIlroy.