Predicting the Spatially Varying Infection Risk in Indoor Spaces Using an Efficient Airborne Transmission Model

We develop a spatially dependent generalisation to the Wells-Riley model and its extensions applied to COVID-19, that determines the infection risk due to airborne transmission of viruses. We assume that the concentration of infectious particles is governed by an advection-diffusion-reaction equation with the particles advected by airflow, diffused due to turbulence, emitted by infected people and removed due to the room ventilation, inactivation of the virus and gravitational settling. We consider one asymptomatic or presymptomatic infectious person who breathes or talks, with or without a mask and model a quasi-3D setup that incorporates a recirculating air-conditioning flow. A semi-analytic solution is available and this enables fast simulations. We quantify the effect of ventilation and particle emission rate on the particle concentration, infection risk and the `time to probable infection' (TTPI). Good agreement with CFD models is achieved. Furthermore, we derive power laws that quantify the effect of ventilation, emission rate and infectiousness of the virus on the TTPI. The model can be easily updated to take into account modified parameter values. This work paves the way for establishing `safe occupancy times' at any location and has direct applicability in mitigating the spread of the COVID-19 pandemic.