(CNN) Don't go cold turkey -- at least not when it comes to easing lockdown restrictions.
That's the message of a new study that uses mathematical modeling to show that governments shouldn't just turn off lockdown measures all at once for everyone, after infection rates have slowed, unless they want to risk a spike in coronavirus cases that threatens to overwhelm their health care system.
"Decision makers -- pay attention to the math: emerging from lockdowns requires a gradual and phased approach to keep infection under control," said Michael Bonsall from the Mathematical Ecology Research group at the University of Oxford, who helped lead the study team.
"Without this attention, you run the risk of burdening health systems with further waves of infection," Bonsall told CNN.
Lockdown restrictions, or "anti-contagion strategies," have varied from country to country and state to state but include travel bans, school closures, work from home/stay at home orders, quarantining and isolation. They can reduce infection rates, spreading infections over a longer period in an approach known as flattening the curve.
Thanks to lockdown measures, an estimated 60 million coronavirus infections were prevented in the United States, and 285 million in China, according to a separate study recently published in the journal Nature.
But lockdowns have huge emotional costs and have crippled economies across the globe, including officially plunging the United States into a recession.
As spread of the coronavirus shows signs of slowing down in some parts of the world, governments -- and individual states in the US -- are grappling with how to reopen society without catastrophically driving up infection rates again.
The study, published Wednesday in the journal Frontiers in Public Health, compared simply ending restrictions for everyone all at once to a more gradual approach. The goal was to allow the greatest number of people to return to work while -- critically -- keeping the rate of new infections low enough so as not to overwhelm the health care system.
The results show that the optimal strategy would be to release about half of the population two to four weeks after the end of infection peak while keeping as much social distancing as possible, and then wait another three to four months -- to let a possible second peak pass -- before releasing the second group. Widespread testing would also have to take place, to monitor infection rates and how well the disease is controlled.
"Furthermore, to increase the number of people that can be first released, lockdown should not be ended until the number of new daily confirmed cases reaches a sufficiently low threshold," the research team wrote in their report.
The model isn't foolproof; it depends heavily on two variables that are hard to pin down precisely. "We show that for the gradual release strategy that two model parameters -- the infection rate and the recovery rate (or fatality rate) from the virus -- are the biggest unknowns that influence our predictions," said Bonsall.
"We also modelled an 'on-off' strategy, of releasing everyone, but re-establishing lockdown if infections become too high. We conclude that the worst-case scenario of a gradual release is more manageable than the worst-case scenario of an on-off strategy," the group added in their report.
Even though the model focused on the population of the UK and the capacity of its health care system, it can be used in countries large and small, Bonsall said.
"The model is general and can be applied, with different parameters, across different countries and within regions/states within countries," Bonsall said. The researchers did not specify which groups should be released first, but in the paper suggested younger people, who are on the whole less susceptible to getting severely ill. There are also other ways of dividing the population, said Bonsall.
"Deciding which groups get released might depend on critical functions to the economy, decisions about education over economy growth, critical functions to local economies," he said. "It also might be decided based on geography," he added.
"This has huge ramifications and is all out of scope of our work but obviously critical to implementing the findings by decision makers."
Dr. Amesh Adalja, an infectious disease doctor and a senior scholar at Johns Hopkins Center for Health Security, says transmission of the virus will certainly go up as people start to emerge from lockdown.
"You have to realize the virus isn't going to go anywhere; it's going to be present in that, as social mobility increases ... you're going to see an uptick in cases," he told CNN. "The question will be, what is the trade-off between that uptick in case and the other aspects of people's lives. How do you make that trade-off?"
Adalja said as long as hospitals have the capacity to treat the seriously ill patients, it's up to individuals to decide what to do. "The only real exit strategy is going to be a vaccine, but because that's not going to come from maybe two years or so, you have to make a decision on how you want to move forward," he said.
As for the particular path for emerging from lockdown that is outlined in the paper, he said, in the US it is already too late, because many existing restrictions have already been loosened greatly in many places.
"I worry sometimes the models get overly interpreted as the only way forward and people forget that they're not," he added. "As we move into an exit strategy, it's clear we're going to get more cases. It's just that we want to make sure that our social distancing recommendations are titrated for what's going on in hospitals, so that we don't get into a position like we saw in New York City in March."