The effect of local ventilation on a spatiotemporal model of airborne disease transmission in indoor spaces

Pretty, Alexander, Griffiths, Ian M., Lau, Zechariah and Kaouri, Katerina ORCID: https://orcid.org/0000-0002-9850-253X 2026. The effect of local ventilation on a spatiotemporal model of airborne disease transmission in indoor spaces. European Journal of Applied Mathematics 10.1017/s0956792526100485

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Abstract

We incorporate local ventilation effects into a spatially dependent generalisation of the Wells–Riley model for airborne disease transmission and consider a room in which an air purifier supplements the ventilation provided by a poorly functioning air-conditioning (AC) unit. Aerosol production and removal through ventilation, biological deactivation and gravitational settling as well as transport around a recirculating AC flow and global turbulent mixing are modelled using an advection–diffusion–reaction equation. This local ventilation model is compared with a global ventilation model, where all ventilation is treated as a global sink. We undertake this comparison for a weak purifier (clean air delivery rate of 140 m3h−1) and a strong purifier (clean air delivery rate of 1,000 m3h−1). For each purifier, we determine a total effective air exchange rate and compare against the global model with equivalent ventilation. We find that, as expected, the purifier removes fewer aerosols when the distance between the infectious person and the purifier is increased, resulting in a greater average aerosol concentration in the room. Moreover, the concentration is generally lowest when the infectious person is upstream of the purifier, located in regions where the airflow streamlines are directed into the purifier. For these infectious source locations, the global ventilation model significantly overestimates the concentration throughout the room. For infectious sources outside of these regions, there is generally good agreement between the models, particularly for the weak purifier. We also studied, for a fixed distance from the purifier, how the infection risk to a susceptible person varies as the infectious person changes location. A susceptible person faces the highest infection risk when they are directly downstream of the infectious person, where the aerosol concentration is the highest. There is better agreement between local and global ventilation models for the weak purifier than for the strong purifier since the weak purifier has less impact on the airflow in the room.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	Cambridge University Press
ISSN:	0956-7925
Date of First Compliant Deposit:	20 July 2026
Last Modified:	20 Jul 2026 15:45
URI:	https://orca.cardiff.ac.uk/id/eprint/188353

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