The Zika epidemic in Latin America could be over within three years, scientists have said.
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.
Peruvian officials have declared a Zika health emergency across the northern half of their country after confirming that 102 people have been infected with the virus.
The 90-day emergency was announced in the official gazette El Peruano, which said the health ministry and local authorities were working to prevent the spread of the disease.
The cases detected so far include 34 pregnant women.
Zika is seen as a cause of microcephaly, abnormally small heads and brains, in babies.
A major Zika outbreak in neighbouring Brazil, where nearly 1,600 babies have been born with the birth defect, has prompted concerns for athletes and visitors ahead of the Olympic Games in Rio de Janeiro next month.
There is growing evidence that in limited cases Zika can also be transmitted sexually.
In adults and children it usually causes only mild, flu-like symptoms and a rash.
But it has been linked to neurological problems such as a potentially fatal paralysis known as Guillain–Barré Syndrome.
Professor Neil Ferguson, from the School of Public Health at Imperial College London, said the study published today "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.