Charles E. and Emma H. Morrison Professor of Economics, Weinberg College of Arts & Sciences; Professor of Managerial Economics & Decision Sciences (Courtesy)
As schools and businesses consider whether they can reopen safely, many are exploring rotation plans, in which groups of students or employees take turns inhabiting the physical space. The basic ideas behind rotation are simple: bringing fewer people together allows for easier social distancing, while staggering schedules can help minimize transmission of COVID-19.
“When you don’t know whether an infection has started in an organization—and if it has, how far along it’s progressed—you can still try to manage the spread of this invisible potential infection by controlling who interacts with whom,” says Jeffrey Ely, a professor of managerial economics and decision sciences (courtesy) at the Kellogg School, who is also a professor of economics at Northwestern.
But as appealing as rotation plans may seem, public health officials have said little about how organizations should implement them. Leaders are therefore left guessing about even the most basic decisions, such as how frequently they should rotate between groups—daily, weekly, monthly? And are these schemes even worth the effort in large organizations, since some intermixing between the rotation groups is virtually inevitable?
New research from Ely and colleagues provides concrete guidance to organizations grappling with these questions.
Working with Andrea Galeotti of London Business School and Jakub Steiner of the University of Zurich, Ely uses mathematical models to simulate several possible rotation schedules. The researchers then pinpoint which plan is best suited for which type of organization, based on how equipped the organization is to detect and react quickly to infections.
They find that for organizations with a quick reaction time, the optimal strategy is frequent rotation—say, dividing your staff into two groups, and having each come into the office on alternating days. But for organizations that are slower to respond, the optimal strategy is minimal rotation—say, having one group come into the office for a month straight, then the other group for the next full month.
In both scenarios, the rotation plan will minimize the number of healthy people who come into contact with infected people on average, meaning that fewer new infections can arise in the time between when a person is infected and when the organization can detect their infection and instruct them to quarantine.
Importantly, the researchers also find that a rotation plan doesn’t need to be perfect in order to be beneficial. While intermixing between groups is not ideal, a small amount of mixing should not dramatically exacerbate the spread of the disease, they conclude.
“If you do it mostly right, you’re going to get the benefit,” says Ely.
The researchers imagine an organization with 2,000 people, who are divided into two equally-sized groups, Group A and Group B. The two groups will take turns being in the same physical space during the pandemic.
In the researchers’ scenario, one person in the organization may be infected. But—crucially—it takes some time before the organization can learn whether there is an infection, and, if so, whether the infected individual is in Group A or Group B.
This slow reaction time parallels the real world, Ely explains. Some people with COVID-19 are initially asymptomatic, and even those people experiencing symptoms may be reluctant to speak up, since it could lead to them missing work or school. Even when tests are readily available, results typically take several days to come back. Plus, he adds, “the organization itself might not have the decision-making infrastructure to act right away.”
An organization’s reaction time—the total number of days between the onset of an infection and leaders becoming aware of it—is what determines how frequently the organization should rotate between groups.
In the researchers’ model, they assume that members of the organization can only spread the infection to one another if they’re in the space together (although, as is the case in real life, individuals may also contract the infection from other people outside of the organization).
So, in order to minimize the spread of the virus, how often should the two groups rotate out?
The researchers’ models revealed that an organization’s reaction time—the total number of days between the onset of an infection and leaders becoming aware of it—is what determines how frequently the organization should rotate between the rotation groups.
To see why reaction time determines the optimal rotation schedule, Ely says, imagine that you’re the leader of the hypothetical organization that has just decided to begin rotating the two groups, but has not yet determined how frequently.
Assume, for the sake of example, that Group A has been coming into the building for the past six days (not as part of a rotation scheme, but simply in the usual course of business). Now you must decide what should happen on day seven, the first day of the new rotation schedule: should Group A come in for another day, or should Group B rotate in?
First, imagine that the company has a robust testing plan where, in case of an infection, it will take only two days for the company to learn about it.
“The important thing about that two-day reaction time is that on this seventh day, since you haven’t seen anything yet, you know the infection didn’t happen seven days ago,” Ely says, “and you know it didn’t happen six days ago. If it did happen, it happened at most two days ago. And in two days, it’s very unlikely that there’s been a lot of transmission” relative to the size of the organization, since the short timespan limits the number of interactions that could have taken place.
Consequently, after six days in the building, Group A has a relatively small number of individuals who have been infected; the vast majority are still healthy. However, since the virus may have already had a day or two to spread, the number of sick people—who could spread the virus to others—is greater than it was when the virus first arrived in the group. This unfortunate combination—lots of healthy targets, plus a fast-growing number of carriers—could lead the infection to spread quite quickly from here on. “So one extra day for this group is quite costly in terms of new infections,” Ely says.
Group B, on the other hand, also has plenty of healthy potential targets—but, since they have not been in the space together, the number of infections is likely to be lower, meaning that the virus (if present) will spread more slowly in this group, on average. Thus, the researchers find, it’s better to bring in Group B on day seven.
However, after day seven, each group will be in the opposite predicament. Now any potential infection (which, again, may or may not exist) has had a full day to spread through Group B, meaning this group could now have the bad combination of lots of healthy targets and a fast-growing number of spreaders. But, since Group A was safely quarantined at home, you can be confident that there were no new transmissions among its members—and, thanks to the quick detection time, you can quarantine anybody who was infected two or more days ago. Thus, if there are any new, undetected infections in Group A (i.e., those resulting from people socializing outside of work or school), they will not yet have spread through the group at all, meaning there are few carriers.
At this point, bringing back Group B again will likely result in more infections than bringing in Group A, so the company will want to rotate in Group A on day eight—and so on. On every subsequent day, the “safer” group will be the one that was quarantined the day before; thus, the optimal strategy is to rotate between the two groups daily.
By doing so, you halve the time that a hitherto-undetected infection is able to spread in either group; on average, the researchers confirm, this strategy will minimize transmission.
Now imagine a bleaker scenario: due to a shortage of testing, it takes 10 days for the company to become aware of an infection.
In this case, after day six, “you don’t know whether there’s been an infection,” Ely explains. “But you do know that if there has been, it’s quite likely that enough time has passed that very many of these individuals are infected. And now you’re in this grisly situation where you basically have a lot of infected people interacting with a lot of infected people.”
Since there is now relatively little room for the virus to spread, the “cost” of keeping Group A in the building for another day is relatively low—on average, it will produce fewer new infections than bringing in Group B, for whom a latent infection could spread dramatically in one day, since the vast majority of them are healthy.
Again, the same logic will hold on day eight and every day thereafter until the virus has been neutralized. Thus, a longer rotation schedule—say, swapping between Group A and Group B once a month (or even less frequently)—is the best way to stem the total spread of the virus given a slow reaction time.
“Small deviations from perfect rotation have a negligible impact on the spread of the disease. So don’t be too concerned about doing it 100 percent right.”
Ely emphasizes that this slow rotation schedule does not necessarily mean that an entire group will get sick (again, the model assumes that the organization has imperfect information and cannot be sure whether there is an infection until several days after the fact). But, in reality, if someone starts showing symptoms, then an organization should immediately isolate them and anyone they came into contact with, he notes.
While the researchers kept their analysis to two rotation groups for simplicity, Ely notes that the idea remains the same if there are more than two groups. He recommends that organizations use social distancing guidelines to calculate the maximum number of people their space can safely accommodate at one time, which will, in turn, dictate how many groups are needed. “If you need to reduce your presence by 50 percent, then you want to rotate two groups,” he explains. “If it’s 33 percent, then you want to rotate three groups. And so on.”
In the researchers’ theoretical model, the two rotation groups remain perfectly separated. However, Ely acknowledges that this is not always possible in the real world.
“There might be some individuals who just have to be there all the time, and so that’s some mixing you can’t avoid,” he says. “Or you might have some people take a day off, and maybe you want to fill their spot with a member of the other group.”
When the researchers allow for this kind of intermixing in their mathematical models, they find that it leads to higher rates of transmission, on average, than no mixing at all. This is what they expected, Ely explains, since rotation plans minimize transmission by increasing the odds that most infected people interact with other infected people, and most healthy people with healthy people; mixing, on the other hand, makes it more likely that the sick and healthy will interact.
However, the math reveals that a small amount of mixing is unlikely to exacerbate the spread of the virus. For instance, they find that if an organization of 100 people is rotating daily between Group A and Group B, and 10 percent of people are infected, swapping members between the groups should lead to no more than one extra infection in total, on average.
That finding might be of particular interest to school administrators, given that some districts are planning to assign each teacher to multiple groups of students.
“Small deviations from perfect rotation have a negligible impact on the spread of the disease,” Ely says. “So don’t be too concerned about doing it 100 percent right.”