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

We incorporate local ventilation effects into a spatially dependent generalisation of the Wells--Riley model for airborne disease transmission. Aerosol production and removal through ventilation, biological deactivation, and gravitational settling as well as transport around a recirculating air-conditioning flow and turbulent mixing are modelled using an advection--diffusion--reaction equation. The local ventilation model, motivated by air purifiers, is compared with the global ventilation model for a weak purifier (CADR = 140 m$^3$h$^{-1}$) and a strong purifier (CADR = 1,000 m$^3$h$^{-1}$). We find that, as expected, increasing the distance of the infectious person from the purifier reduces the aerosol concentration. 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 inlet. 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 fixed distance from the purifier, how the infection risk to a susceptible person varies as the infectious person changes location. The infection risk is greatest when the susceptible person is directly downstream of the infectious person. There is better agreement between local and global ventilation models for the weak purifier than the strong purifier.