Predicting the spatio-temporal infection risk in indoor spaces using an efficient airborne transmission model

We develop a spatially dependent generalization to the Wells-Riley model, which determines the infection risk due to airborne transmission of viruses. We assume that the infectious aerosol concentration is governed by an advection-diffusion-reaction equation with the aerosols advected by airflow, diffused due to turbulence, emitted by infected people, and removed due to ventilation, inactivation of the virus and gravitational settling. We consider one asymptomatic or presymptomatic infectious person breathing or talking, with or without a mask, and model a quasi-three-dimensional set-up that incorporates a recirculating air-conditioning flow. We derive a semi-analytic solution that enables fast simulations and compare our predictions to three real-life case studies-a courtroom, a restaurant, and a hospital ward-demonstrating good agreement. We then generate predictions for the concentration and the infection risk in a classroom, for four different ventilation settings. We quantify the significant reduction in the concentration and the infection risk as ventilation improves, and derive appropriate power laws. The model can be easily updated for different parameter values and can be used to make predictions on the expected time taken to become infected, for any location, emission rate, and ventilation level. The results have direct applicability in mitigating the spread of the COVID-19 pandemic.