Modelling airborne transmission of SARS-CoV-2 using CARA: risk assessment for enclosed spaces

Abstract

The COVID-19 pandemic has highlighted the need for a proper risk assessment of respiratory pathogens in indoor settings. This paper documents the COVID Airborne Risk Assessment methodology, to assess the potential exposure of airborne SARS-CoV-2 viruses, with an emphasis on virological and immunological factors in the quantification of the risk. The model results from a multidisciplinary approach linking physical, mechanical and biological domains, enabling decision makers or facility managers to assess their indoor setting. The model was benchmarked against clinical data, as well as two real-life outbreaks, showing good agreement. A probability of infection is computed in several everyday-life settings and with various mitigation measures. The importance of super-emitters in airborne transmission is confirmed: 20% of infected hosts can emit approximately two orders of magnitude more viral-containing particles. The use of masks provides a fivefold reduction in viral emissions. Natural ventilation strategies are very effective to decrease the concentration of virions, although periodic venting strategies are not ideal in certain settings. Although vaccination is an effective measure against hospitalization, their effectiveness against transmission is not optimal, hence non-pharmaceutical interventions (ventilation, masks) should be actively supported. We also propose a critical threshold to define an acceptable risk level.

Keywords: CARA; COVID-19; SARS-CoV-2; airborne transmission; modelling; risk assessment.

Figure 1.

Results of the MCS of the viral emission rate distribution for an infected host breathing, speaking and shouting, while undertaking sedentary physical activity (seated) and comparing with the viral load distribution. Dashed lines correspond to the mean of the log₁₀ values. The vertical axis of the histograms corresponds to the estimation of distribution PDFs. Median vR^total values: 3, 67 and 349 virion h⁻¹ for breathing, speaking and shouting, respectively. The values are without the effect of face covering (η_out = 0).

Figure 2.

Results of the viral concentration profile over the exposure time and the cumulative absorbed dose, in the classroom scenario, for different combination of measures. The solid lines represent the concentration (left y-axis) and the dotted lines represent the cumulative dose (right y-axis). The horizontal section of the dotted lines correspond to the breaks (starting t = 2 and t = 7 h for 30 min in the playground and t = 4 h for 1 h lunch), where the infected and exposed hosts leave the room and are not in contact for the duration. Panel (a) illustrates the scenarios with different natural ventilation scenarios and (b) the effect of HEPA filtration and masks. Note that the scale of both y-axes differ in the two panels (a,b). For visualization purposes, the confidence interval is not represented in the figure; these values can be found in electronic supplementary material, table S.4.

Figure 3.

Probability of infection in the ski cabin scenario, and related dependency on the viral load. Results assume the index host was infected with the delta VOC and none of the occupants were vaccinated. (i) Expected probability of infection for a given viral load value, with mean (solid line) and 90% CI (shaded area). Comparison between the baseline scenario (blue curve) and situations with stricter set of measures. The X markers denote the critical viral load vl_{crit,p≤0.05} in each situation. The dotted line corresponds to the hypothetical viral load of the infected (index) host. (ii) Histogram of the viral load data from [23]. The vertical axis corresponds to the probability density function of the adopted distribution. The dotted line indicates the hypothetical viral load of the infected (index) host. (iii) Set of histograms of the conditional probability of infection P(I|vl), one for each scenario, showing the results of the MCS, including the integration on the full range of viral load data in [23]. The P(I) values shown in the middle of each histogram plot indicate the full probability (as per equation (2.19)).

Figure 4.

Comparison of the viral emission rate from this study with those reported in outbreaks. SARS-CoV-2 (model) reflects the result from the MCS for a light physical activity and different expiratory activities (breathing, speaking, shouting). The violin plots denote the histograms of vR^total, with the bottom and top bars indicating the 5th and 95th percentiles and the larger bar between indicating the mean. Literature data (recorded outbreaks) is a collection of emission rate values published by Mikszewski et al. [91], with values in infectious quanta (following the Wells–Riley approach adopted by the authors), converted into virions, normalized with an infection coefficient by multiplying the values in table 3 of [91] with the infectious dose distribution used in this study (vR^total = quanta × ID₅₀/ln(2)). The boxplots illustrate the result of this quanta-to-virion conversion, denoting the mean (IQR), minimum and maximum values of each distribution.

Figure 5.

Conditional probability of infection P(I|vl), with a 90% CI (blue shaded area). vl_crit,a and vl_crit,b are the critical threshold values up to which the probability of infection is close to 0 and 1, respectively, dividing the range of viral loads into three shaded regions (in green, orange and red).

Figure 6.

Probability of infection depending on the absorbed dose of infectious virus (vD). Comparison between the real-life outbreak scenario at the Skagit Valley Chorale event [83] and how it would relate to the epidemiological conditions 18 months into the pandemic. The solid blue line represents the model results of real-life scenario, with the shaded area corresponding to a 90% CI. The other solid/dashed lines represent the conditions with different VOCs and vaccination status. The boxplots indicate the distribution of vD for the real-life scenario and with a hypothetical ventilation improvement for comparison, with the box descriptors indicating the mean (IQR) and the whiskers indicating 5th and 95th percentiles.