Modelling uncertainty in the relative risk of exposure to the SARS-CoV-2 virus by airborne aerosol transmission in well mixed indoor air

Abstract

We present a mathematical model and a statistical framework to estimate uncertainty in the number of SARS-CoV-2 genome copies deposited in the respiratory tract of a susceptible person, $\sum n$ , over time in a well mixed indoor space. By relating the predicted median $\sum n$ for a reference scenario to other locations, a Relative Exposure Index (REI) is established that reduces the need to understand the infection dose probability but is nevertheless a function of space volume, viral emission rate, exposure time, occupant respiratory activity, and room ventilation. A 7 h day in a UK school classroom is used as a reference scenario because its geometry, building services, and occupancy have uniformity and are regulated. The REI is used to highlight types of indoor space, respiratory activity, ventilation provision and other factors that increase the likelihood of far field ( $>2$ m) exposure. The classroom reference scenario and an 8 h day in a 20 person office both have an $\mathrm{REI}\simeq 1$ and so are a suitable for comparison with other scenarios. A poorly ventilated classroom (1.2 l s^-1 per person) has $\mathrm{REI}>2$ suggesting that ventilation should be monitored in classrooms to minimise far field aerosol exposure risk. Scenarios involving high aerobic activities or singing have $\mathrm{REI}>1$ ; a 1 h gym visit has a median $\mathrm{REI}=1.4$ , and the Skagit Choir superspreading event has $\mathrm{REI}>12$ . Spaces with occupancy activities and exposure times comparable to those of the reference scenario must preserve the reference scenario volume flow rate as a minimum rate to achieve $\mathrm{REI}=1$ , irrespective of the number of occupants present.

Keywords: Airflow; Classroom; Infection; School; Ventilation.