There is no doubt that the world has changed as a consequence of COVID-19. As infections rapidly increased many countries, including the UK, implemented ‘lockdown’. While we can all see this significantly reduces virus transmission, eventually a return to some kind of normality is required and attention is turning to what constitutes a safe release from lockdown.

Professor Chris Huntingford, a climate change modeller at the UK Centre for Ecology and Hydrology, and honorary senior research associate at the University of Oxford, is a mathematician by training. Chris has been able to apply his mathematical expertise to the national emergency research effort, and alongside colleagues at the University, they have been modelling optimum release strategies. Chris explains…

The extent of change we’ve witnessed and experienced in recent weeks as a result of COVID-19 is quite remarkable. Most lives are affected in one way or another. Therefore, while the last three weeks have been personally quite difficult - modelling illness and even deaths is never going to be easy and is a far cry from what I am used to - it was an honour to be invited to work with a team, led from the University of Oxford’s Mathematical Ecology Research Group, and play a part in developing some of the potential ways out of this crisis.

Together we modelled optimum lockdown release strategies. A starting point for this is a form of equations called a Susceptible-Exposure-Infection-Recovery (SEIR) model, which describes how people pass through the various stages of an illness. Critically it contains a transmission rate parameter, and this characterises how infections spread. We applied the SEIR model to two sets of people; those in ‘lockdown’ or quarantine as we termed it, and where modelled transmission is low, and a non-quarantine community initially made up of essential workers. In the computer model, sets of people are released from the quarantine group at different stages, and as they return to employment, the number of new infections is estimated. The modelling system can also allow for a simulated return of full lockdown measures.

The challenge was to solve the equations optimally, subject to constraints. One way to do this through a form of ‘control theory’, which can be likened to setting a car Satnav. You can ask for the best way to get from A to B, with constraints of the shortest distance, or maybe instead using motorways to give a faster but longer route.

There is a balance to be struck, especially given the damage to lives, health and livelihood associated with economic damage - Professor Chris Huntingford

Here, the question was what form of graded release from lockdown could maximise those returning to work, but with the constraint of never overwhelming the health service? Based on details particular to the UK, the headline finding is that the optimal strategy is to wait until substantially past the initial peak, before allowing roughly half of the population to return to work. Infections will then inevitably rise but could be manageable by the health service. Once this second peak has subsided, which is expected to take around three months, then the second set of people can be released.

Our analysis implies that, when optimised in this way, strategies that manage the exit from lockdown via a graded release of people are more effective than those that cycle the entire population through periods of quarantine and release. Such cycles, sometimes referred to as the "On/Off" strategy, are to cope with infections rising rapidly after times of full release.

There is no acceptable level of deaths from COVID-19 and so these calculations may appear callous. But unfortunately there is a balance to be struck, especially given the damage to lives, health and livelihood associated with economic damage.

It seems logical that to minimise COVID-19 related deaths, then lockdown would need to continue until either a vaccine exists, or it has washed fully out of the UK. But, in reality we know that’s probably just not possible. Indeed, as is often pointed out (but may as yet need quantification) without a functioning economy, an all-encompassing health service cannot exist, which is essential to support all our healthcare needs. We, therefore, need to identify the safest way possible to ease lockdown, while protecting lives and livelihoods.

Chris Huntingford

Further information

View the preprint of the paper, titled “How and when to end the COVID-19 lockdown: an optimisation approach” by Thomas Rawson, Tom Brewer, Dessislava Veltcheva, Chris Huntingford and Michael Bonsall.

The University of Oxford issued a press release about the preprint paper.

Update 11 June 2020: This analysis was published as a peer-reviewed, open access paper on 10 June 2020 in Frontiers in Public Health. DOI: 10.3389/fpubh.2020.00262