The team from Cambridge University and Imperial College London developed a mathematical model to help predict the risk of disease transmission, which was validated with a controlled experiment in a real train carriage. The team’s findings also show that masks are more effective than social distancing at reducing transmission, particularly in trains not ventilated with fresh air.
The research, reported in Indoor Air, shows how challenging it is to for individuals to calculate absolute risk, and how important it is for train operators to improve their ventilation systems to help keep passengers safe.
COVID-19 restrictions have been lifted in the UK, but the government continues to highlight the importance of good ventilation in reducing the risk of transmitting the disease, as well as other respiratory infections such as influenza.
“In order to improve ventilation systems, it’s important to understand how airborne diseases spread in certain scenarios, but most models are very basic and can’t make good predictions,” said first author Rick de Kreij, who completed the research while based at Cambridge’s Department of Applied Mathematics and Theoretical Physics. “Most simple models assume the air is fully mixed, but that’s not how it works in real life.
“There are many different factors which can affect the risk of transmission in a train – whether the people in the train are vaccinated, whether they’re wearing masks, how crowded it is, and so on. Any of these factors can change the risk level, which is why we look at relative risk, not absolute risk – it’s a toolbox that we hope will give people an idea of the types of risk for an airborne disease on public transport.”
The researchers developed a one-dimensional (1D) mathematical model which illustrates how an airborne disease can spread along the length of a train carriage. The model is based on a single train carriage with closing doors at either end, although it can be adapted to fit different types of trains, or different types of transport, such as planes or buses.
The 1D model considers the essential physics for transporting airborne contaminants, while still being computationally inexpensive.
The model was validated using measurements of controlled carbon dioxide experiments conducted in a full-scale railway carriage, where CO2 levels from participants were measured at several points. The evolution of CO2 showed a high degree of overlap with the modelled concentrations.
The researchers found that air movement is slowest in the middle part of a train carriage.
“If an infectious person is in the middle of the carriage, then they’re more likely to infect people than if they were standing at the end of the carriage,” said de Kreij. “However, in a real scenario, people don’t know where an infectious person is, so infection risk is constant no matter where you are in the carriage.”
The researchers are now looking to extend their 1D-model into a slightly more complex, yet still energy-efficient, zonal model, where cross-sectional flow is characterised in different zones. The model could also be extended to include thermal stratification, which would offer a better understanding of the spread of an airborne contaminant.
The research was funded in part by the Engineering and Physical Sciences Research Council.