key: cord-293301-7bmj8qsv
authors: Buonanno, Giorgio; Stabile, Luca; Morawska, Lidia
title: Estimation of airborne viral emission: quanta emission rate of SARS-CoV-2 for infection risk assessment
date: 2020-04-17
journal: nan
DOI: 10.1101/2020.04.12.20062828
sha: 
doc_id: 293301
cord_uid: 7bmj8qsv

Airborne transmission is a pathway of contagion that is still not sufficiently investigated despite the evidence in the scientific literature of the role it can play in the context of an epidemic. While the medical research area dedicates efforts to find cures and remedies to counteract the effects of a virus, the engineering area is involved in providing risk assessments in indoor environments by simulating the airborne transmission of the virus during an epidemic. To this end, virus air emission data are needed. Unfortunately, this information is usually available only after the outbreak, based on specific reverse engineering cases. In this work, a novel approach to estimate the viral load emitted by a contagious subject on the basis of the viral load in the mouth, the type of respiratory activity (e.g. breathing, speaking), respiratory physiological parameters (e.g. inhalation rate), and activity level (e.g. resting, standing, light exercise) is proposed. The estimates of the proposed approach are in good agreement with values of viral loads of well-known diseases from the literature. The quanta emission rates of an asymptomatic SARS-CoV-2 infected subject, with a viral load in the mouth of 108 copies mL-1, were 10.5 quanta h-1 and 320 quanta h-1 for breathing and speaking respiratory activities, respectively, at rest. In the case of light activity, the values would increase to 33.9 quanta h-1 and 1.03×103 quanta h-1, respectively. The findings in terms of quanta emission rates were then adopted in infection risk models to demonstrate its application by evaluating the number of people infected by an asymptomatic SARS-CoV-2 subject in Italian indoor microenvironments before and after the introduction of virus containment measures. The results obtained from the simulations clearly highlight that a key role is played by proper ventilation in containment of the virus in indoor environments.

Expiratory human activities generate droplets, which can also carry viruses, through the atomization 38 processes occurring in the respiratory tract when sufficiently high speeds are reached (Chao et al., 39 2009; Morawska, 2006) . Indeed, during breathing, coughing, sneezing or laughing, toques of liquid 40

originating from different areas of the upper respiratory tract are drawn out from the surface, pulled 41 thin, and broken into columns of droplets of different sizes (Hickey and Mansour, 2019) . The content 42 of infectious agents expelled by an infected person depends, among other factors, on the location 43 within the respiratory tract from which the droplets originated. In particular, air velocities high 44 enough for atomization are produced when the exhaled air is forced out through some parts of the 45 respiratory tract which have been greatly narrowed. The front of the mouth is the site of narrowing 46 and the most important site for atomization; since most droplets originate at the front of the mouth, 47 the concentration of an infectious agent in the mouth (sputum) is representative of the 48 concentration in the droplets emitted during the expiratory activities (Morawska, 2006) . Thus, 49 knowledge of the size and origin of droplets is important to understand transport of the virus via 50 the aerosol route. Contrary to the findings of early investigations (Duguid, 1945; Jennison, 1942 ; 51 Wells, 1934) , subsequent studies involving optical particle detection techniques capable of 52 measurements down to fractions of a micrometer suggested that the majority of these particles are 53

in the sub-micrometer size range (Papineni and Rosenthal, 1997) . More recently, the growing 54 availability of higher temporal and spatial visualization methods using high-speed cameras (Tang et 55 al., 2011), particle image velocimetry (Chao et al., 2009 ) and, above all, increasingly accurate particle 56

counters (Morawska et al., 2009 ) allowed the detailed characterization and quantitation of droplets 57 expelled during various forms of human respiratory exhalation flows (e.g. breathing, whispering, 58 speaking, coughing). Therefore, in recent years a marked development has occurred both in the 59 techniques for detecting the viral load in the mouth and in the engineering area of the numerical 60 simulation of airborne transmission of the viral load emitted. 61

However, the problem of estimating the viral load emitted, which is fundamental for the simulation 62 of airborne transmission, has not yet been solved. This is a missing "transfer function" that would 63 allow the virology area, concerned with the viral load values in the mouth, to be connected with the 64 aerosol science and engineering areas, concerned with the spread and mitigation of contagious 65 particles. 66

A novel approach is here presented for estimating the viral load emitted by an infected individual. 67

This approach, based on the principle of conservation of mass, represents a tool to connect the 68 medical area, concerned with the concentration of the virus in the mouth, to the engineering area, 69 dedicated to the simulation of the virus dispersion in the environment. On the basis of the proposed 70 approach, the quanta emission rate data of SARS-CoV-2 were calculated as a function of different 71 respiratory activities, respiratory parameters, and activity levels. 72

The quanta emission rate data, starting from the recently documented viral load in sputum 73

(expressed in copies mL -1 ), were then applied in an acknowledged infection risk model to investigate 74 the effectiveness of the containment measures implemented by the Italian government to reduce 75 the spread of SARS-CoV-2. In particular, airborne transmission of SARS-CoV-2 by an asymptomatic 76 subject within pharmacies, supermarkets, restaurants, banks, and post offices were simulated, and 77 the reduction in the average number of infected people from one contagious person, R0, was 78 estimated. 79

The approach proposed in the present work is based on the hypothesis that the droplets emitted 82 by the infected subject have the same viral load as the sputum. Therefore, if the concentration of 83 the virus in the sputum and the quantity of droplets emitted with dimensions less than 10 µm is 84 known, the viral load emitted can be determined through a mass balance. In particular, the viral 85 load emitted, expressed in terms of quanta emission rate (ERq, quanta h -1 ), was evaluated as: 86 87

(1) 88

where cv is the viral load in the sputum (RNA copies mL -1 ), Vbr is the volume of exhaled air per breath 89 (cm 3 ; also known as tidal volume), Nbr is the breathing rate (breath h -1 ), Nd is the droplet number 90 concentration (part. cm -3 ), and Vd(D) is the volume of a single droplet (mL) as a function of the 91 droplet diameter (D). Information about the viral load in terms of quanta is essential as the quantum 92 represents the "viral load" considered in engineering science: in other words, an infected individual 93

constantly generates a number of infectious quanta over time, where a "quantum" is defined as the 94 dose of airborne droplet nuclei required to cause infection in 63% of susceptible persons. 95

The volume of the droplet (Vd) was determined on the basis of data obtained experimentally by 96 (Morawska et al., 2009 ): they measured the size distribution of droplets for different expiratory 97

activities (e.g. breathing, whispering, counting, speaking), recognizing that such droplets present 98 one or more modes occurring at different concentrations. In particular, in the study a particle size 99 distribution with four channels was considered with midpoint diameters of D1=0.8, D2=1.8, D3=3.5, 100

and D4=5.5 µm. As an example, speaking was recognized as producing additional particles in modes 101 near 3.5 and 5.5 µm. These two modes became even more pronounced during sustained 102

vocalization. Details of the aerosol concentrations at the four channels of the size distribution during 103 each expiratory activity are reported in (2) 110

where j indicates the different expiratory activities considered (namely whispered counting, voiced 111 counting, speaking, breathing) and IR (m 3 h -1 ) is the inhalation rate, i.e. the product of breathing 112 rate (Nbr) and tidal volume (Vbr), which is a function of the activity level of the infected subject. The 113 quanta emission rate from equation (2) can vary in a wide range depending on the virus 114 concentration in the mouth, the activity level, and the different types of expiration. Regarding the 115 inhalation rate effect, the quanta emission rate calculations are shown for three different activity 116 levels (resting, standing, and light exercise) in which the inhalation rates, averaged between males 117 and females, are equal to 0.36, 0.54, and 1.16 m 3 h -1 , respectively (Adams, 1993; International 118 Commission on Radiological Protection, 1994). 119

The pandemic of a novel human coronavirus, now named Severe Acute Respiratory Syndrome 121

CoronaVirus 2 (SARS-CoV-2 throughout this manuscript), emerged in Wuhan (China) in late 2019 122 and then spread rapidly in the world (https://www.who.int/emergencies/diseases/novel-123 coronavirus-2019). In Italy, an outbreak of SARS-CoV-2 infections was detected starting from 16 124 cases confirmed in Lombardy (a northern region of Italy) on 21 February. The Italian government 125 has issued government a decree dated 11 March 2020 concerning urgent measures to contain the 126 contagion throughout the country. This decree regulated the lockdown of the country to counteract 127 and contain the spread of the SARS-CoV-2 virus by suspending retail commercial activities, with the 128 exception of the sale of food and basic necessities. It represents the starting point of a system with 129 imposed constraints. Among the measures adopted for the containment of the virus in Italy, great 130 importance was placed on the safe distance of 1 m (also known as "droplet distance"). This distance 131 was actually indicated by the World Health Organization as sufficient to avoid transmission by air, 132

without any reference to the possibility of transmission over greater distances indoors 133 (https://www.who.int/emergencies/diseases/novel-coronavirus-2019). With this measure, along 134 with the opening of only primary commercial establishments (such as pharmacies, supermarkets, 135 banks, post offices) and the closure of restaurants, the Italian government has adopted the concept 136 of spacing (known as "social distancing") to prevent the spread of the infection. Obviously, this limit 137 per se would have no influence on the reduction of airborne transmission of the infection in indoor 138 environments since this distance is compatible with the normal gathering of people in commercial 139 establishments. Actually, on an absolutely voluntary basis, and despite the continuous denials by 140 the government on the risk of indoor airborne transmission, commercial associations have changed 141

the methods of accessing their commercial spaces such as restaurants, pharmacies, supermarkets, 142 post offices, and banks; for example, by forcing customers to queue outside. It is clear that the best 143 choice in containing an epidemic is a total quarantine which, however, appears to have enormous 144 costs and social impacts, especially in Western countries. 145 To The indoor microenvironments considered here were a pharmacy, supermarket, restaurant, post 153 office, and bank whose dimensions are summarized in Table 2 . Two different exposure scenarios 154

were simulated for each microenvironment: before lockdown (B) and after lockdown (A). In the 155 simulation of the scenario before lockdown, the microenvironments were run with no particular 156 recommendations; thus, people enter the microenvironments and queue indoors, often resulting in 157 overcrowded environments. Since most of the indoor microenvironments in Italy are not equipped 158 with mechanical ventilation systems, the simulations were performed considering two different 159 situations: natural ventilation (a typical value for an Italian building equal to 0.2 h -1 was adopted, both natural ventilation and mechanical ventilation; in this case a slight increase in the air exchange 167 rate (AER) for natural ventilation (0.5 h -1 ) was considered in order to take into account that the door 168

was always kept open. The restaurant was not tested in the scenario after lockdown since such 169 commercial activity was closed down as a consequence of the lockdown. For all the scenarios 170 considered in the simulations, the infected individual was considered to enter the 171 microenvironment as the first customer (alone or along with other individuals according to the 172 scenarios summarized in Table 2 ). All the scenarios were simulated taking into account that the virus 173 is able to remain viable in the air for up to 3 hours post aerosolization as recently detected by (van 174

Doremalen et al., 2020); thus, if the infected individual remained inside the environment for 10 175 minutes (e.g. pharmacy), the calculation of the quanta concentration, infection risk, and R0 was 176 performed for up to 3 hours and 10 minutes (named "total exposure time" in Table 2 ). For 177 restaurants the calculation was performed for 3 hours considering that after 3 hours (i.e. two groups 178 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint . https://doi.org/10.1101/2020.04.12.20062828 doi: medRxiv preprint remaining inside for 1 hour and 30 minutes one after the other) the microenvironment was left 179 empty. 180 and Nucci model is based on the rate of change in quanta levels through time; in particular, the 192 differential equations for the change of quanta in a control volume as well as the initial conditions 193 (here not reported for the sake of brevity) allowed to evaluate the quanta concentration in an 194

indoor environment at the time t, n(t), as: 195

where AER (h -1 ) represents the air exchange rate of the space investigated, n0 represents the initial 197 number of quanta in the space, I is the number of infectious subjects, V is the volume of the indoor 198 environment considered, and ERq is the abovementioned quanta emission rate (quanta h -1 ) 199 characteristic of the specific disease/virus under investigation. 200

The equation was derived considering the following simplifying assumptions: the quanta emission 201 rate is considered to be constant, the latent period of the disease is longer than the time scale of 202 the model, and the droplets are instantaneously and evenly distributed in the room (Gammaitoni 203 and Nucci, 1997). The latter represents a key assumption for the application of the model as it 204

considers that the air is well-mixed within the modelled space. The authors highlight that in 205 epidemic modeling, where the target is the spread of the disease in the community, it is impossible 206 to specify the geometries, the ventilation, and the locations of the infectious sources in each 207 microenvironment. Therefore, adopting the well-mixed assumption is generally more reasonable 208 than hypothesizing about specific environments and scenarios because the results must be 209 interpreted on a statistical basis (Sze To and Chao, 2010). 210 To where IR is the inhalation rate of the exposed subject (which is, once again, affected by the subject's 215 activity level) and T is the total time of exposure (h). From the infection risk R, the number of 216 susceptible people infected after the exposure time can be easily determined by multiplying it by 217 the number of exposed individuals. In fact, equations (3) and (4) were adopted to evaluate the 218 infection risk of different exposure scenarios of Italian microenvironments hereinafter reported. 219

The quanta emission rate used in the simulation of the scenario represents the average value 220 obtained from the four expiratory activities (whispered counting, voiced counting, speaking, and 221 breathing); the data are reported and discussed in the result sections. 222

As discussed in the Materials and methods section, the quanta emission rate, ERq, depends on 225 several parameters. In Figure 1 the ERq (quanta h -1 ) trends are reported as a function of the viral 226 load in the sputum (cv, RNA copies mL -1 ) for different expiratory activities (whispered counting, 227 voiced counting, speaking, breathing) and different activity levels (resting, standing, light exercise). 228 To represent the large variabilities (over several orders of magnitude) of ERq as a function of cv, the 229 graph is reported on a bi-logarithmic scale. 230 To benchmark the proposed approach for the estimation of the quanta emission rate, we 231 considered the case of seasonal influenza for which more data are available in terms of both viral 232 load in sputum and quanta emission rate. As an example, (Hirose et al., 2016) found an average 233 value of RNA concentration in sputum for influenza equal to 2.38×10 7 copies mL -1 . Thus, applying 234 the findings of the proposed approach in the case of a standing subject, a corresponding ERq varying 235 between 3.7 (breathing) and 114 quanta h -1 (speaking) is estimated: this value is in good agreement 236

with the quanta emission rates for influenza found in the scientific literature, from 2 to 128 237 quanta h -1 with a most frequent value of 67 quanta h -1 (Knibbs et al., 2012) . Such variability in the 238 quanta emission rates for influenza is due both to the method used to calculate it (Rudnick and 239 Milton, 2003) and, especially, the viral load of the subject and the type of respiratory activity, which 240 is typically not reported and discussed. 241 242 243 

Light exercise quanta emission rates (ERq) for a SARS-CoV-2 infected asymptomatic subject as a function of activity 255 level (resting, standing, and light exercise) and respiratory activity (voiced counting, whispered  256 counting, speaking, breathing). The data confirm the huge variations in the quanta emission rate, 257

with the lowest value being for breathing during resting activity (10.5 quanta h -1 ) and the highest 258 value being for speaking during light activity (more than 1000 quanta h -1 ). 259 Table 3 -Quanta emission rates (ERq) for a SARS-CoV-2 infected asymptomatic subject (cv=10 8 copies mL -1 ) 260 as a function of the activity level and respiratory activity. 

In this section, the results of the simulations performed for the microenvironments and exposure 263 scenarios described in section 2.2 and summarized in Table 2 are reported. 264

As an illustrative example, Figure 2 shows the quanta concentration (n(t)) and infection risk (R) 266 trends as a function of time for two different exposure scenarios simulated for the pharmacy, i.e. 267 before lockdown (B) in natural (NV) and mechanical ventilation (MV) conditions. The trends clearly 268

highlight that the presence of the infected individual remaining inside for 10 minutes leads to an 269 increase in the quanta concentration in the volume: in particular, a higher peak of quanta 270 concentration was recognized, as expected, for reduced ventilation (NV) with respect to the 271 mechanical ventilation (MV). People entering the pharmacy after the infected individual are 272 exposed to a certain quanta concentration during their 10-min time, and the resulting risk for their 273 exposure (evaluated through equation (4)) is just a function of the quanta concentration trend. For 274 example, people entering the microenvironment around the quanta concentration peak are at a 275 higher risk than people entering the pharmacy later. Figure 2 shows an example of a customer 276 entering at min 26 and leaving at min 36: the risk for this 10-min exposure is 2.4% in natural 277 ventilation conditions and 1.0% in mechanical ventilation conditions. During the entire exposure 278 time of such a scenario (3 hours and 10 minutes), 179 customers (after the infected individual) enter 279 the pharmacy and each of them receive their own risk. In particular, the average risk of the 179 280 customers is 2.0% for NV conditions and 0.4% for MV conditions, then leading to a R0 (among the 281 customers) of 3.52 and 0.68, to which must be added the R0 of the five pharmacists exposed for the 282 entire period. Similar trends, not shown here graphically for the sake of brevity, were obtained for 283 all the scenarios investigated, then leading to the evaluation of the R0 for each of them as described 284

in the methodology section. 285 286 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint . https://doi.org/10.1101/2020.04.12.20062828 doi: medRxiv preprint Table 2 ). The R0 data were calculated for an 295 asymptomatic SARS-CoV-2 infected subject (cv=1×10 8 copies mL -1 ) while standing; in particular, the 296 average ERq value among the different respiratory activities was considered (147 quanta h -1 , Table  297 3). The exposed subjects were also considered to be standing (IR=0.54 m 3 h -1 ). The new regulations and methods of accessing the indoor environments that were applied in the 315 conditions after lockdown (i.e. queuing outside, limited time spent in the environments, lower 316 crowding index) were very effective; indeed, the R0 values were reduced by roughly 80%-90% (for 317 both natural and mechanical ventilation conditions) with respect to the corresponding pre-318 lockdown scenarios. 319

As an example, for the natural ventilation scenario, the only critical microenvironment was the bank, 320

since the R0 was >1; this was due to a crowding index that was higher than the post-office, which 321 had a larger floor area but same number of customers. In contrast, all the R0 values for indoor 322 environments equipped with mechanical ventilation systems were much lower than 1 (0. The values obtained with this approach could vary significantly as a function of (i) the activity levels 330

of both the infected subject and the exposed subjects; and (ii) the viral load in the sputum of the 331 infected subject; therefore, in future studies, more specific exposure scenarios could be simulated 332 on the basis of the findings proposed and discussed in this study. 333 334 335 Figure 3 -R0 calculated for all the exposure scenarios (natural ventilation, mechanical ventilation; before 336 lockdown, after lockdown) and microenvironments (pharmacy, supermarket, restaurant, post office, bank) 337 under investigation considering an asymptomatic SARS-CoV-2 infected subject (cv=1×10 8 copies mL -1 ) while 338 standing (IR=0.54 m 3 h -1 ; ERq=147 quanta h -1 ) and the exposed population, also standing. 

The present study proposed the first approach aimed at filling the gap of knowledge still present in 341 the scientific literature about evaluating the viral load emitted by infected individuals. This 342 information could provide key information for engineers and indoor air quality experts to simulate 343 airborne dispersion of diseases in indoor environments. To this end, we have proposed an approach 344 to estimate the quanta emission rate (expressed in quanta h -1 ) on the basis of the emitted viral load 345 from the mouth (expressed in RNA copies in mL -1 ), typically available from virologic analyses. Such 346 approach also takes into account the effect of different parameters (including inhalation rate, type 347 of respiratory activity, and activity level) on the quanta emission rate. The suitability of the findings 348 was checked and confirmed as it was able to predict the values of quanta emission rates of previous 349

well-known diseases in accordance with the scientific literature. The proposed approach is of great 350 relevance as it represents an essential tool to be applied in enclosed space and it is able to support 351 air quality experts and epidemiologists in the management of indoor environments during an 352 epidemic just knowing its viral load, without waiting for the end of the outbreak. 353

For this purpose, it has been applied to the Italian case which, at the time of writing, represents the 354 country with the highest number of deaths from SARS-CoV-2 in the world, highlighting the great 355 importance of ventilation in indoor microenvironments to reduce the spread of the infection. 356 357 358

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