By Jillian Kunze
When individuals who are carrying an airborne disease—such as COVID-19 or influenza—move around a space, they expel infectious aerosol particles that can infect other people in the area. These aerosols can move with airflow and remain suspended for hours, which makes the problem of understanding disease transmission extremely complex.
“In future epidemics, policymakers would need to make fast decisions to mitigate transmission based on scientific input,” Yidan Xue of Cardiff University said. During a minisymposium presentation at the 2024 SIAM Conference on the Life Sciences—which is taking place this week in Portland, Ore.—Xue described the development of a novel modeling framework and web app that will help policymakers determine how best to mitigate the risk of infectious diseases in indoor spaces.
Xue is a postdoctoral researcher in the epidemic modeling team led by Katerina Kaouri and Thomas Woolley at the Cardiff University School of Mathematics. The researchers teamed up with Wassim Jabi of the Welsh School of Architecture at Cardiff University—who developed an advanced spatial modeling and analysis software for architecture, engineering, and construction called topologicpy—to model the movement schedule of individuals within several indoor spaces. The model makes several assumptions: For instance, it assumes that the infectious individual is a moving point source of aerosols, and that people emit aerosols of the same size at a rate that is based on their activity. The room is not well-mixed, and the concentration of aerosols is temporally and spatially dependent. The aerosols also reflect perfectly off walls.
The collaborators set the governing equations for an agent-based model, in which each agent (an individual person, in this case) follows a particular trajectory. They used a susceptible-infected-recovered (SIR) model to track the number of individuals who were susceptible to, infected by, and recovering from the disease. A reaction-diffusion equation, implemented with a fast finite element solver, is assumed to govern the aerosol concentration. Each person’s risk of catching the disease varies across space and time, so the team used the Lau et. al. model (an extension of the Wells-Riley model) to define the spatiotemporal infection risk. “The next step is to construct the architectural information,” Xue said. Through topologicpy, the researchers built three-dimensional spaces and connected them topologically; the software was then able to automatically construct a navigation graph to control people’s movements through the space.
Animation 1. A simulation of six people moving within a care home. One person is infectious at the start, but three additional people become infected throughout the course of the day. Animation courtesy of Yidan Xue.
Each person in the model possesses several attributes, such as their movement speed, whether they are infectious or susceptible to disease, what activity they are performing, and whether they are wearing a mask. “Each person can also have their own schedule,” Xue said. Topologicpy computes their movements along the shortest paths between their predetermined locations of interest.
The team is currently constructing a user-friendly web app that will be freely available for both policymakers and the general public to explore different infection mitigation strategies in indoor areas, following from their policy work during the COVID-19 pandemic. Starting with the geometry of the location’s architecture, the web app adds the schedules of every individual within the population, then incorporates the physics of aerosol spread. The app only requires a few seconds to compute the results for an entire day’s schedule.
Xue provided several example scenarios for the web app, starting with a hearing in a courtroom. The people in this scenario undertake actions like talking, talking loudly, or resting. The collaborators were able to use their novel model to simulate this situation and analyze the impact of different potential mitigation strategies. They found that providing better ventilation reduces the infection risk, as does wearing masks (particularly N-95 masks).
Figure 1. The simulated infectious aerosol concentration within a small grocery store. Hot spots of higher aerosol concentration are evident within the top plot. In the bottom plot, the ventilation of the space is improved by about 10 times in terms of the air changes per hour (ACH), which eliminates the hot spots. Figure courtesy of Yidan Xue.
The second example simulation was a care home, based on the floor plan of an actual care home in the U.K. Animation 1 depicts a scenario with six people, one of whom is initially infected. Throughout the course of the day, three additional people become infected as they move around the building. Critically, the researchers could keep the same movement simulation but vary which person was initial infected to investigate who was safest or most at risk during their daily lives, and extract features from their schedules that cause their risks to diverge. The model also demonstrated that understandably, reducing the amount of time spent in common rooms decreased the infection risk.
Finally, Xue provided an example of a small supermarket. Infectious people create hotspots of aerosols (where the aerosol concentration is higher) in areas where they linger — particularly around the checkout. Reducing the number of shelves only slightly reduced the risk, since the amount of time that individuals were spending in the store did not change; the hot spots just moved location. Improving the ventilation of the space did help mitigate the infection risk, however (see Figure 1), and exploring the impact of adding air purifiers could be an interesting future addition.
Overall, the agent-based modeling framework and associated web app can quickly assess the impact of ventilation, masks, schedules, and building layouts on each person’s infection risk. The web app is scheduled to publicly launch this upcoming July. “For future work, it will be nice to consider flow pattern models,” Xue said, adding that doing so could incorporate the direction in which people are facing and other spatial considerations. The collaborators also hope to look at heat flow, integrate their model with energy analysis, and try to model multistory buildings. “The last thing is model calibration and refinement with a more real-world data,” Xue said. “For this, we will leverage collaborations with policymakers, space managers, and architects.”
Acknowledgements: This work is done in collaboration with the Welsh government and funded by an Engineering and Physical Sciences Research Council Impact Acceleration Account grant.
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Jillian Kunze is the associate editor of SIAM News. |