Researchers from the University of Oxford’s Department of Zoology and the UK Centre for Ecology & Hydrology have adapted a Susceptible-Exposure-Infection-Recovery (SEIR) framework to test the efficacy of two possible lockdown release strategies. The UK was used as a test case. 

Findings from this research showed that a gradual re-integration approach – wherein small portions of the population are released from lockdown measures over a long period of time after infection levels fall below a critical level – will ensure that infection surges are prevented.

Alternatively, testing of the “on-off” strategy – wherein everyone is released from lockdown simultaneously and lockdown is reinstated if infections surge too high – demonstrated a high risk of causing new waves of reinfection with a high likelihood of a reinstitution of lockdown measures.

According to the pre-print manuscript, the optimal gradual re-integration strategy would entail the release of half the UK population approximately two to four weeks after the end of an initial infection peak. After waiting three to four months to allow a second infection peak, the rest of the population would be released

The research, led by Professor Michael Bonsall from the University’s Department of Zoology, applied an optimal control framework to their adapted SEIR framework.

Professor Bosnall explained: “This is a mathematical model that groups people into different classes – (S) susceptible (not had the disease), (E) exposed (infected but not infectious – captures a class of individuals who have the infection but aren’t able to transmit it), (I) infected (individuals who are infectious can spread the disease to susceptible individuals) and (R) recovered individuals.

“We adapted this framework to have two groups – a group in lockdown/quarantine and a group not in lockdown. Those in lockdown have a lower probability of spreading disease than those not in lockdown. We use a mathematical approach to look for optimal solutions – with the question – how can we release the group in lockdown without increasing infections beyond a critical threshold (aka the number of beds in the NHS for COVID patients).”

Two factors are key for a successful lockdown release strategy: keeping the virus spread rate down and ensuring a quick recovery rate. The former can be ensured by social distancing, hand-washing, and limiting exposure to people outside one’s household, while the latter is achieved through scientific discovery and active improvement of the treatment of coronavirus. The research team acknowledged that accurate tracking of these two factors is essential to efficiently monitor the pandemic. 

Professor Bosnall emphasised that mathematical models like his team’s adapted SEIR model should be used for advice but cannot act as a single solution for government approaches to lockdown release. He advocates the synthesis of evidence from a variety of disciplines in all cases in which governments seek science-related advice and particularly in finding an appropriate and effective lockdown release strategy.

Professor Bosnall said: “Mathematical models require careful [parameterisation] and the results can be skewed by inaccurate values – exploring the sensitivity of our predictions to changes in parameters is another way to provide weight of evidence – if changing spread rate has very little effect on the general prediction that gradual exit from lockdown is best, then we can be robust in this advice.“We are using epidemiological studies in Oxford and elsewhere to collect data on the levels of infection in the community. This is essential to understand the background levels of virus infections, inform our models and help deliver appropriate public health planning.”