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

Zechariah Lau,Ian M Griffiths,Katerina Kaouri,Aaron English

doi:10.1098/rspa.2021.0383

Abstract

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.

Highlights

The COVID-19 pandemic has spread rapidly across the globe, with more than 245 million confirmed cases worldwide and almost five million deaths, at the time of writing [1]
Computational Fluid Dynamics (CFD) models are useful in studying airborne transmission as they take into account the room size, geometry, complex turbulent airflow, and size distribution of the aerosols
Taking I = 0.0069 corresponds to an emission rate of 62 quanta/h. This provides a spatially averaged probability of 39%, which matches well with four people infected by P1 out of nine. (Note that our quanta emission value is approximately half of the quanta emission rate of 130 quanta/h found by back-calculation in [30] using the Wells–Riley model.) In table 4 we present the dose inhaled by each person normalized by the dose inhaled by P2, who was closest to P1, as well as the infection risk

Summary

Introduction

The COVID-19 pandemic has spread rapidly across the globe, with more than 245 million confirmed cases worldwide and almost five million deaths, at the time of writing [1]. Following [38], we model an infected person who is breathing or talking as a continuous point source emitting virus-carrying aerosols at a constant rate of R aerosols/s. The airborne transmission models in [24,27,35,62] all use different values for Rtotal, following [63–66], respectively; these values are compiled in table 1 Some of these papers present the emission rate in terms of number of aerosols per volume of breath exhaled, RV = Rtotal/ρinf, where ρinf is the average breathing rate of the infectious person. We will use the dimensionless parameter R = R/R0, where R0 is the rate of emission of infectious aerosols when breathing (see tables 2 and 3) In this way, the results may be scaled when better estimates of R become available.

Comparing the model with real-life case studies

Hypothetical case study: a classroom

Findings

Conclusion and future directions