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. 2020 Oct 30;15(10):e0241539.
doi: 10.1371/journal.pone.0241539. eCollection 2020.

Modeling the load of SARS-CoV-2 virus in human expelled particles during coughing and speaking

Yang Wang  1 , Guang Xu  2 , Yue-Wern Huang  3
Affiliations

Modeling the load of SARS-CoV-2 virus in human expelled particles during coughing and speaking

Yang Wang et al. PLoS One. .

Abstract

Particle size is an essential factor when considering the fate and transport of virus-containing droplets expelled by human, because it determines the deposition pattern in the human respiratory system and the evolution of droplets by evaporation and gravitational settling. However, the evolution of virus-containing droplets and the size-dependent viral load have not been studied in detail. The lack of this information leads to uncertainties in understanding the airborne transmission of respiratory diseases, such as the COVID-19. In this study, through a set of differential equations describing the evolution of respiratory droplets and by using the SARS-CoV-2 virus as an example, we investigated the distribution of airborne virus in human expelled particles from coughing and speaking. More specifically, by calculating the vertical distances traveled by the respiratory droplets, we examined the number of viruses that can remain airborne and the size of particles carrying these airborne viruses after different elapsed times. From a single cough, a person with a high viral load in respiratory fluid (2.35 × 109 copies per ml) may generate as many as 1.23 × 105 copies of viruses that can remain airborne after 10 seconds, compared to 386 copies of a normal patient (7.00 × 106 copies per ml). Masking, however, can effectively block around 94% of the viruses that may otherwise remain airborne after 10 seconds. Our study found that no clear size boundary exists between particles that can settle and can remain airborne. The results from this study challenge the conventional understanding of disease transmission routes through airborne and droplet mechanisms. We suggest that a complete understanding of the respiratory droplet evolution is essential and needed to identify the transmission mechanisms of respiratory diseases.

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Conflict of interest statement

No authors have competing interests.

Figures

Fig 1
Fig 1
Evolution of droplets emitted by a cough over an elapsed time of ten seconds at respiratory viral loads of (a–c) 7.00 × 106 and (d–f) 2.35 × 109 copies per ml. (a) and (d) Size distribution of droplets and virus-containing droplets at point of emission. (b) and (e) Size distribution of non-virus-containing (airborne), virus-containing (airborne), and settled particles at an elapsed time of ten seconds. (c) and (f) Distribution of vertical distances traveled by the virus-containing particles at an elapsed time of ten seconds. The inset figure in panel (c) shows a schematic of the modeled system.
Fig 2
Fig 2. Evolution of droplets emitted by one-minute of speaking after an elapsed time of ten seconds at a respiratory viral load of 2.35 × 109 copies per ml.
(a) Size distribution of droplets and virus-containing droplets at point of emission during one-second of speaking. (b) Size distribution of non-virus-containing (airborne), virus-containing (airborne), and settled particles at an elapsed time of ten seconds. (c) Distribution of vertical distances traveled by the virus-containing particles at an elapsed time of ten seconds. (d) Size-dependent filtration efficiency curves for a surgical mask (earloop) extracted from Chen et al. [42] and Hao et al. [43]. (e) Size distribution of non-virus-containing (airborne), virus-containing (airborne), and settled particles at an elapsed time of ten seconds with mask-wearing. (f) Distribution of vertical distances traveled by the virus-containing particles at an elapsed time of ten seconds with mask-wearing.
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Grants and funding

YW, GX, and YH are supported by the U.S. National Science Foundation (nsf.gov) grant 2034198. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.