After March and April were filled with angst as the number of cases and deaths attributed to COVID-19 grew exponentially, Europeans are now experiencing a much-needed breather. However, the dangers of the coronavirus still loom, and lifting lockdowns without a proper strategy could spell a disastrous second wave that could be much worse than the first.

In a new study published in the journal Frontiers in Public Health, researchers at the University of Oxford and the UK Centre for Ecology and Hydrology in Wallingford devised a complex mathematical model that analyzed the outcomes of various lockdown-lifting strategies.

“We have interest in my group on optimal control – how to find the best solution to a problem given some constraints. Here we were super motivated to get an understanding of how to emerge from lockdown (given a mathematical model for disease spread) with the constraint we didn’t want to overburden the health system (ie. total number of ICU beds),” Professor Michael Bonsall from the Mathematical Ecology Research Group at the University of Oxford told ZME Science.

“The main finding is that emergence from lockdown must proceed gradually to avoid infection resurging. Our model suggests releasing people in two waves rather than all at once to avoid overburdening health systems.”

For their model, the researchers looked at the numbers of susceptible, exposed, infectious, and recovered (or deceased) persons in the UK in order to find the best strategy to come out of lockdown without overwhelming the national health system — something estimated to happen when there are approximately 4 million infected people in the country.

You can never predict accurately how people will behave at the individual level, but when grouped together, a population’s behavior is much more predictable. Bearing this in mind, the researchers devised algorithms that can solve optimal control math problems.

Out of all possible strategies, the authors concluded that the most optimal approach is to release approximately half of the population out of lockdown 2-4 weeks after an initial peak in infections. After 3-4 months of careful monitoring and testing, the other half of the population can be allowed to move without restrictions. The first wave of lockdown relaxation should involve the least at-risk population, in this case, young people and those without a history of chronic illness, followed by the rest of the population in the second wave.

What’s the worst strategy you might ask? That would simply be releasing everyone out of lockdown in one single wave.

“In our case, the worst strategy is to let everyone out straightway (without any distancing) – this on-off strategy results in infections resurging really quickly and then a need to reimpose lockdown,” Bonsal said.

“Our optimal strategy is to do releases gradually – the model is applicable at a range of scales – city, country, region. So we can evaluate how release from lockdown should proceed based on new infections as they are reported,” he added.

As a caveat, this mathematical model is based on imperfect assumptions about both population behavior and the coronavirus’ infectious characteristics. Because the virus’ rate of transmission and population susceptibility to infection are not set in stone, the model’s outcomes have to be taken with a grain of salt.

However, Bonsal says that his team is working hard so their model is optimal in real-time in order to provide decision-makers with immediately actionable strategies.

“The take-home message for decision-makers is to act very cautiously, and to monitor any lockdown release very closely. Our model shows that second waves can occur very quickly if transmission rates end up higher than expected, or if more people relax their lockdown measures than expected. The delayed incubation period between infection and presenting symptoms means that we are constantly seeing the effect of the disease a few days late. Only by ramping up testing measures can we accurately get a sense of how the spread and control of disease is happening. This will allow us to respond quickly if an unmanageable second wave begins to appear,” concludes Dr. Thomas Rawson from the University of Oxford, the first author of the new study.