Zonal modeling of air distribution impact on the long-range airborne transmission risk of SARS-CoV-2

A widely used analytical model to quantitatively assess airborne infection risk is the Wells-Riley model which is limited to complete air mixing in a single zone. However, this assumption tends not to be feasible (or reality) for many situations. This study aimed to extend the Wells-Riley model so that the infection risk can be calculated in spaces where complete mixing is not present. Some more advanced ventilation concepts create either two horizontally divided air zones in spaces as displacement ventilation or the space may be divided into two vertical zones by downward plane jet as in protective-zone ventilation systems. This is done by evaluating the time-dependent distribution of infectious quanta in each zone and by solving the coupled system of differential equations based on the zonal quanta concentrations. This model introduces a novel approach by estimating the interzonal mixing factor based on previous experimental data for three types of ventilation systems: incomplete mixing ventilation, displacement ventilation, and protective zone ventilation. The modeling approach is applied to a room with one infected and one susceptible person present. The results show that using the Wells-Riley model based on the assumption of completely air mixing may considerably overestimate or underestimate the long-range airborne infection risk in rooms where air distribution is different than complete mixing, such as displacement ventilation, protected zone ventilation, warm air supplied from the ceiling, etc. Therefore, in spaces with non-uniform air distribution, a zonal modeling approach should be preferred in analytical models compared to the conventional single-zone Wells-Riley models when assessing long-range airborne transmission risk of infectious respiratory diseases.