How can we get our staff back to work safely and what measures do we need to put in place to make it happen? This is the fundamental quandary occupying the minds of business decision makers throughout the world as lockdown restrictions ease. Finding answers by trial and error is certainly not an option of course, so methods such as computational modelling and simulation provide a compelling case for adoption.

Monitoring people & assets through cutting-edge sensor & algorithm design

Simulations enable the modelling of various courses of action before real-life implementation, where the stakes may be high. Computational methods, meanwhile, are most valuable when it is unethical or unfeasible – because of significant health risks – to conduct equivalent clinical or population studies.  Their ability to evaluate performance, to assess the robustness of the response systems by probing a wide range of parameters, make them powerful tools to support strategic decision making.

Along with a team of colleagues, I’ve developed a simulation tool which could be used by companies looking to get their staff back to work safely and efficiently. The tool helps to confront the likely risks and address the benefits of reduced staff numbers, the removal of communal spaces and the use of contact tracing to monitor the interaction of infected staff. All of these measures can be simulated and lead to a significant reduction in the spread of infection – and keep a business running optimal during the 
pandemic. 

But before we go any further, I must present a caveat. The parameters of the simulations have been set for illustrative purposes only. While the results probably point in the right direction, the data should not be used to draw any real-life conclusions. The model would require more developments and the input of clinical data to correspond accurately to a specific disease. Nevertheless, we’re confident that the tool provides valuable insights to help in the search for the best disease-limiting workplace strategy.

Four states identified by colour

In this simulation, we have modelled the spread of a pandemic in a workplace contaminated by one employee. The model aims to represent the propagation of an airborne disease with a transmission by close contact or distance between individuals. The response of the employees to the disease depends on both their health condition and the ability to detect the disease. This is modelled by four states each identified by a colour:

  • Healthy and susceptible to get infected (green)
  • Infected and not yet detected (orange). This state may also describe individuals who can transmit the disease without showing any symptoms
  • Infected and diagnosed with infection (red)
  • Recovered and immune to the disease (yellow) 

The software simulates the daily schedule of an office where people have an allocated desk and meet randomly to work together (meeting room, workshop, laboratory) or to have a rest (coffee room, kitchen, canteen). When meeting in these common areas, they are assigned a random seat and they can get infected by the colleagues sitting next to them. While sitting in an open plan area, individuals can only be infected by their nearest neighbours. 

The distance between neighbours also plays a role as the probability of infection or transmission reduces with increasing distance. The choice of a probabilistic approach aims at representing the very random nature of infection of airborne diseases in real life, from the chaotic transport of contaminated droplets by turbulent air flows to the contingency of the meetings we attend or the colleagues we bump into every day.

In the simulation presented in the video, the people who have been diagnosed as sick go home immediately. As the simulation progresses, the number of infected/asymptomatic, sick and recovered people are recorded, giving an overview of the effect of a single infected person coming to work. The graph below shows the result of running the simulation ten times and the variations to expect between each run. 

Figure 1: Comparison of ten repeats of a simulation with the same parameters. In this setup, the individuals who are diagnosed with the disease are sent home. The graph shows the variability inherent to the probabilistic simulation and highlights the best- and worst-case scenario, along with the expected trend (sample average). 

The variation in outcomes illustrates both a strength and a limitation of simulations. The strength is that we can get a feel for the variability by running the same simulation many times, as was done above. If the simulations are close, we may assume a higher confidence in our predictions. If there are large variations, we must understand that these outcomes are all possible. 

The limitation is also illustrated: three lines on the graph are highlighted. The centre one is the average result of all simulation runs. It provides a sense of the most likely outcome. However, the higher and lower ones represent two extreme scenarios the system can experience: from the case where the person initially infected can be diagnosed before contaminating everyone and recover, to the worst-case scenario where the peak of infection is at a much higher level than the average prediction. 

A decision-making dilemma

For many types of simulation, there will be a large difference between the lowest and highest outcome, as here. That presents the decision maker with a dilemma: whether to use the average, most likely result, or to be cautious and use the worst-case outcome, even if this is unlikely. Simulations rarely give a definite answer, but most often need interpretation by specialists. 

Now that we have a tool to model how a disease might spread under pre-pandemic conditions, let’s consider some measures that could implemented to mitigate the risks encountered. For this we have run a series of simulations, all with the exact same parameters (number of employees, probabilities of infection and so on) except the mitigating measures investigated. The results are presented in the graph below, in which each curve is the average of 1,000 repeats of the same simulation:

Figure 2: Assessment of strategies to mitigate the spread of the pandemic in the workplace. In this graph, each curve is the sample average of 1,000 repeats of the same implementation. The quadrant on the right-hand side compares the most efficient strategies at a smaller scale.

Reminding the assumptions under which the model has been implemented, the simulations provide the following learnings:

  • Some mitigations can be implemented by structural adaptations of the workplace aiming at limiting contacts between individuals. This may be by halving the maximum number of people allowed simultaneously in meeting rooms, closing the meeting rooms, closing both meeting and coffee rooms (the horror!), or alternating used and empty desks in the open spaces. Surprisingly, the data indicates that limiting access to common rooms does not necessarily reduce the infection peak and can actually have the opposite effect. Indeed, restricting the number of people going to meetings or coffee rooms makes the open plan more filled, which increases the average number of employees sitting around infected ones and therefore exposes them more. On the contrary, increasing the distance between individuals by alternating empty desks in the open space has a very positive impact
  • Mitigations involving a behavioural response of the employees – such as working from home once two people are diagnosed, the contact tracing or sending home the infected people – are particularly efficient at reducing the infection peak. The graph also presents the only simulation in which absolutely no control measures are taken (red curve), and highlights the dramatic effect caused by infected individuals who continue visiting the workplace.
  • The simulation also shows that contact tracing can be as efficient as sending everyone to work from home once a few infected individuals have been detected, while being less disruptive to the workplace

Used with clinical data, such modelling can help assess risk for companies, and help establish strategies to mitigate it. Modelling can assist in the development of a safe return to work plan and minimal interaction to limit the spread of virus. It can identify the key areas of buildings to close off and to limit things like seating numbers to control potential infection.

The approach would be particularly effective coupled to the internal GPS capabilities we’ve developed at Cambridge Consultants. Employees could be tracked throughout the day to identify potential contamination hotspots, with specific colleague interactions recorded. If someone becomes infected, their contacts could be automatically identified – then tested and isolated as necessary.

I think the work is a perfect – and timely – example of how simulations and numerical modelling can support strategic decisions. By quantitatively assessing risks, and weighing up potential solutions, they provide an excellent analytical tool. Please don’t hesitate to drop me an email if you’d like to discuss the topic in more detail. 
 

Author
Baudouin Geraud
Principal Physicist