Mathematical model helps predict the risk of transmission of COVID-19 in a train carriage

Researchers have shown how airborne diseases such as COVID-19 spread along the length of a train carriage and found that there is no “safest place” for passengers to minimize the risk of transmission.

We hope this research will give people an idea of ​​the types of risks for airborne illness in public transportation.”

Rick de Kreij

The researchers, from the University of Cambridge and Imperial College London, developed a mathematical model to help predict the risk of disease transmission in a railcar, and found that in the absence of effective ventilation systems, the risk is the same along its entire length. of the carriage.

The model, which was validated with a controlled experiment in a real train car, also shows that masks are more effective than social distancing at reducing transmission, especially in trains that are not ventilated with fresh air.

The results, reported in the journal indoor airshow how challenging it is for individuals to calculate absolute risk, and how important it is for train drivers to improve their ventilation systems to help protect passengers.

Since COVID-19 is airborne, ventilation is vital to reduce transmission. And while COVID-19 restrictions have been lifted in the UK, the government continues to emphasize the importance of good ventilation to reduce the risk of transmission of COVID-19 and other respiratory infections such as the flu.

“To improve ventilation systems, it is important to understand how airborne diseases spread in certain scenarios, but most models are very basic and cannot make good predictions,” said first author Rick de Kreij, who completed the study. while he worked in Cambridge. Department of Applied Mathematics and Theoretical Physics. “Most simple models assume that the air is completely mixed, but that’s not how it works in real life.

“There are many different factors that can influence the risk of transmission on a train — whether the people on the train are vaccinated, whether they wear masks, how busy it is, etc. Each of these factors can change the risk level, so look into it.” We’re looking at relative risk, not absolute risk — it’s a toolbox that we hope will give people an idea of ​​the types of risks for airborne illness on public transport.”

The researchers developed a one-dimensional (1D) mathematical model that illustrates how an airborne disease, such as COVID-19, can spread along the length of a train car. The model is based on a single train car with closing doors at both ends, although it can be adapted to different types of trains or different types of transport, such as airplanes or buses.

The 1D model takes into account the essential physics for transporting contaminants in the air while still being computationally cheap, especially when compared to 3D models.

The model was validated using measurements from controlled carbon dioxide experiments conducted in a full-size railcar, measuring the participants’ CO2 levels at various points. The evolution of CO2 showed a high degree of overlap with the modeled concentrations.

The researchers found that air movement is slowest in the middle of a train car. “If there is an infectious person in the middle of the carriage, they are more likely to infect people than if they were standing at the end of the carriage,” says de Kreij. “However, in a real-life scenario, people don’t know where an infectious person is, so the risk of infection is constant no matter where you are in the carriage.”

Many commuter trains in the UK are made as cheaply as possible when it comes to passenger comfort – they get the maximum number of seats per carriage. In addition, most commuter trains circulate air instead of bringing in fresh air from the outside, because fresh air must be heated or cooled, which is more expensive.

So if it’s impossible for passengers to know if they’re sharing a train car with an infectious person, what should they do to protect themselves? “Clear as much as possible from the air – physical distancing is not the most effective method, but it does work if the capacity is below 50 percent,” says de Kreij. “And wear a high-quality mask that will protect you not only from COVID-19, but other common respiratory illnesses as well.”

The researchers are now looking to extend their 1D model to a slightly more complex, but still energy-efficient, zonal model, characterizing the cross-sectional flow in different zones. The model could also be extended with thermal stratification, which would provide a better insight into the distribution of an air pollution.

The research was funded in part by the Engineering and Physical Sciences Research Council.


Reference magazine:

de Kreij, RJB, et al. (2022) Modeling disease transmission in a railcar with a simple 1D model. indoor air.

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