One response to dealing with the global pandemic is the practice of rotating employees and students into and out of offices and classrooms to limit the spread of infection.
In a typical case, half the staff or students would be off the premises at any one time and half would be in the office or school. At regular intervals, the two groups would swap places. But how long ought that interval to be?
Public health officials are keen to encourage such rotation – but seem less keen to give guidance on how much time should elapse between changeovers. So, employers and teachers are left with a puzzle. Should rotations be daily, weekly, monthly, or even longer?
We have found that the key to the answer is the ‘reaction time’ of the organisation in question. This is defined as the number of days between an infection and management becoming aware of it.
Put simply, businesses or educational institutions with quick reaction times will best minimise the risk of infection by employing frequent rotations; for example, by bringing in half the staff or students on alternate days. But those with slow reaction times would be better advised to use slow rotations, with perhaps half their people coming into the office for a month, with the other half at home, and vice versa. Optimal strategy
Before examining why this is so, it’s important to bear two things in mind. The first is that both scenarios successfully minimise the risk of healthy people coming into contact with those who have been infected. Neither is ‘better’ than the other; both represent the optimal strategy in quick and slow reaction scenarios.
The second is that rotation plans do not have to be ideal to be beneficial. There is bound to be some slippage between an ideal rotation plan and the one implemented on the ground, but this does not mean big benefits will be absent – imperfect does not mean useless.
To understand why the two scenarios make sense, imagine an organisation where half its people (Group A) have been coming onto the premises for the past six days, not as part of any rotation scheme but in the normal course of things, and the other half (Group B) have not, and those in charge have decided to begin rotations on day seven. How should they decide on the intervals between rotations?
First, take a situation where the company or institution has a quick reaction time, thanks to an efficient and robust testing regime, with those in charge being alerted to an infection within two days of its occurrence. The key fact here is that, on the seventh day, the management knows that, if any infection has taken place, it did so at most two days ago; a period of time that limits the amount of transmission that could have occurred. In other words, Group A has relatively few infected individuals and a vast majority that is still healthy.
That’s the good news. Less welcome is the fact that the virus may already have had one or two days to spread, meaning the numbers infected are already greater than they were when the virus arrived. The situation is one of lots of healthy ‘targets’ and a rapidly growing number of carriers – the ideal scenario for the infection to spread relatively quickly from this point. Every extra day on the premises is likely to prove costly when it comes to new infections.
Of course, Group B also has plenty of healthy targets for the virus but, because they’ve been off site, it’s likely that their infection rate will be lower, meaning a slower average spread of the virus than would have been the case with Group A. Fast vs slow reactors
Research shows that the optimal move is to rotate Group B onto the premises on day seven and rotate Group A off. It may be argued that this simply puts Group B, at the end of the seventh day, in the same position as that which faced Group A 24 hours earlier. And this is quite correct.
Assuming the virus is present, Group B now has the same unwelcome combination of many healthy targets and a rapidly growing number of infected people to spread the disease. Group A, however, has been at home, meaning no new transmissions among the group. (Someone could have been infected on day six, of course, when Group A was still on the premises, but the rapid two-day detection time means any such person can be swiftly quarantined.)
Of course, during the course of spending day seven at home, members of Group A may have been infected through meeting people unconnected with the organisation. But, because they have been at home, the infection will not have spread through the rest of the group.
On day eight, leaving Group B on the premises would be likely to result in more infections, as would have been the case had Group A been left on the premises on day seven. Thus, the correct move now is to rotate Group A back in and Group B out.
The combination of rapid reaction time in the organisation’s testing regime and the daily alternation of the groups halves the length of time in which an undetected infection is able to spread in either group.
This is a very different story for organisations that have considerably slower reaction times; caused perhaps by inadequate testing equipment. As day seven dawns, there’s no way of knowing whether an infection has taken hold in the previous 10 days. If it has, enough time has passed for a considerable number of people to have become infected.
Here, the opposite logic applies to that of the organisation with the rapid reaction time. Insufficient members of Group A are likely to be infected to give the virus little scope to spread further. In this scenario, extra days in the office for Group A do not make a great deal of difference.
By contrast, bringing in Group B on day seven would be likely to see any infections rip through a group of people that has been at home and is thus largely healthy. This danger will persist until the virus has been neutralised; thus the optimal strategy here is to lengthen the rotation period to a month, say, or even longer.
This is the right approach for organisations with slow reaction times – and it’s not necessary for those in charge to wait for test results before acting. If anyone shows symptoms of the virus, they should be isolated straight away, along with anyone with whom they have had contact. Real life
Our work presupposes a neat division into two groups, but real life is rarely so neat. That said, our ideas remain valid if more than two groups are involved.
In such cases, social-distancing guidelines should be used to work out how many people the premises in question can accommodate at any one time. This will then tell the business or institution in question the number of groups required.
For example, should it be necessary to halve the number of people on the premises at any one time, then, as in the previous examples, two rotating groups will be needed; whereas if only 33% of the staff or students can safely remain on site, three groups would be needed. This principle can be applied to any requirement for reduction in numbers.
If our division into two groups does not always reflect reality, then neither does the fact that our model assumes that Group A and Group B are kept entirely separate, almost hermetically sealed from each other.
The fact is that some mixing between the groups is inevitable, whether it is by senior managers and specialists who have to be on the premises permanently to facilitate the smooth running of the organisation, or a member of the other group brought in to plug gaps in the staff, perhaps caused by sickness or holiday.
The bad news is that research shows that this sort of intermingling leads to higher rates
of infection, as may have been expected. The good news is that, certainly in cases of daily rotation, this increase is very modest. Improving the odds
In our first case study above of the fast-reacting company, assuming a total workforce of 100, 10% of whom are infected, swapping members between groups should, on average, lead to no more than one extra infection.
Rotation schemes may seem more than a little complex, but their aim is to increase the odds that infected people mix with other infected people and healthy people mix with other healthy people. It’s really as simple as that. Andrea Galeotti is Professor of Economics at London Business School