# SARS-CoV-2 Aerosol Transmission Indoors: A Closer Look at Viral Load, Infectivity, the Effectiveness of Preventive Measures and a Simple Approach for Practical Recommendations

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## Abstract

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^{8}viral copies/mL. Based on mathematical simplifications of our approach to predict the probable situational attack rate (PARs) of a group of persons in a room, and valid assumptions, we provide simplified equations to calculate, among others, the maximum possible number of persons and the person-related virus-free air supply flow necessary to keep the number of newly infected persons to less than one. A comparison of different preventive measures revealed that testing contributes the most to the joint protective effect, besides wearing masks and increasing ventilation. In addition, we conclude that absolute volume flow rate or person-related volume flow rate are more intuitive parameters for evaluating ventilation for infection prevention than air exchange rate.

## 1. Introduction

#### State of the Art

_{2}emission of room occupants, as well as general air quality requirements or thermal loads within the room.

^{6}viral copies per ml can be measured in the days before symptom onset for the wild-type and the Alpha variant. In some patients, a viral load of up to 10

^{12}viral copies per ml was also found around symptom onset. The temporal dynamic of the viral load depends on the course of the infection. Shortly before or at the onset of symptoms, infected persons carry the highest viral load (peak load). For approximately 10% of the infected persons, a raised peak load of ≥10

^{8}viral copies per ml was found. Within approximately 24 h, the viral load can increase by a factor of about 100. Whether a given patient is infectious can be estimated through measuring the probability to culture the virus. In [13] it is described that viral loads of 10

^{6}, 10

^{7}and 10

^{8}viral copies per ml taken from the swab have a culture probability in a lab of 20%, 50% and 75%, respectively. With the Delta variant, the situation is somewhat different. The mean viral load is around 10

^{8}viral copies per ml, significantly higher viral loads were found and the viral load decreases significantly more slowly after the peak [16,17,18,19].

^{−1}= 63.2%. Hence, a quantum can be seen as a combination of the amount of emitted virus-laden aerosol particles and the critical dose, which may result in an infection in 63.2% of the exposed persons. The quantum concept and Equation (3) were combined by Riley [23] to obtain Equation (4).

_{b,in}), and the duration of stay (t), but is inversely related to the air change rate (λ

_{ACH}) and the room volume (V).

_{0}[25].

_{ind}.

_{Pers}) exactly this percentage of people becomes infected, we define the attack rate (AR) in a given situation as the situational predicted attack rate, PAR

_{S}(see Equation (6)).

_{g}) and the time (t). Overall lambda thereby consists of the air change rate as well as the decay rates because of sedimentation and inactivation. The relative concentration (c

_{rel}) based on the steady-state concentration can be seen as an increase in the concentration compared to the volume flow.

- The filter efficiency of the fabric;
- The leakage (i.e., air flow bypassing the mask) during exhalation;
- The leakage during inhalation.

^{3}/h) was found by Córdova and Latasa [52]. To measure the airflow without movement restrictions, a helmet was used by Jiang et al. [53] in 32 subjects (16 males, 16 females) during speaking with different volumes, as well as during singing.

^{3}/h for low activity (breathing while sitting, standing, talking) [56].

^{7}viral copies/mL, 92% for 10

^{4}to 10

^{7}viral copies/mL and 43% for lower viral loads. The value for the highest viral load was also confirmed by Lindner et al. [61], but seems pretty high for the other groups compared with the values found in the aforementioned studies. In most cases, where the infected person was not detected with the rapid test, the viral load was lower than 10

^{6}viral copies/mL. In [63], it was shown that suitable test kits have a sensitivity of 80% compared with RT-PCR at a viral load of 10

^{6}viral copies/mL. Even the least sensitive test showed a 90% probable detection rate at a viral load of 23·10

^{7}viral copies/mL. Similar orders of magnitude were found in [64]. Of 122 rapid antigen tests investigated by Scheiblauer et al. [65], 96 passed a limit of 75% sensitivity at a viral load of 10

^{6}viral copies/mL. No significant change in the test sensitivity for the VOC was found [66,67]. In a model [68] as well as a longitudinal study [69], it was shown that rapid antigen tests are able to detect infected persons during the course of an infection and may therefore reduce the transmission [68] if performed at a regular frequency [69]. Whereas the viral load can increase by a factor of about 100 within 24 h before symptom onset/peak viral load [13], rapid antigen tests will detect an infection only within the diagnostic window around the highest peak of infection. It is therefore possible for an individual to receive a negative test result for a rapid antigen test despite being infected and even contagious for other persons. For this reason, an increase in regular testing frequency can greatly increase the significance of a negative test result of a rapid antigen test compared with a negative result obtained with sporadic testing. It was shown in [70] that students who had close contact with a classmate who tested positive for SARS-CoV-2 and were subsequently tested daily avoided days absent from school, with no impact on overall infection incidence.

- What viral loads are necessary to infect others via aerosol?
- Which are the most influencing factors regarding airborne transmission?
- Can a risk assessment model be simplified to allow practical recommendations?
- Is there a possibility to implement a simple measurement system for infection risk?
- What is the impact of different prevention measures on the risk of airborne transmission?

## 2. Materials and Methods

#### Dose–Response Model to Predict the Individual Infection Risk and the Predicted Attack Rate (PAR)

_{inh}, in Equation (5) can be described with the help of Equation (8). S

_{V}is thereby the viral-emission rate in viral copies/time and $\frac{{\mathrm{S}}_{\mathrm{V}}}{{\mathsf{\lambda}}_{\mathrm{g}}\xb7{\mathrm{V}}_{\mathrm{R}}}$ is the viral concentration per cubic meter of air. The overall lambda consists of the air change rate (ACH = λ

_{ACH}), the decay rate because of inactivation (λ

_{in}) and the decay rate because of sedimentation (λ

_{sed}).

_{inh}can be reduced. This reduction can be implemented into Equation (11) as factor f

_{M}, which will result in Equation (12).

_{ind}approximates statistically to P

_{q}(Equation (16)), Equation (17) can be obtained, where PAR

_{S}i

_{s}defined as the situational predicted attack rate, the attack rate during a stay in a room with infected persons.

_{0}; second, the parameter C

_{R}, which takes the boundary conditions of the room as well as the time of stay into account; third, the breathing volume flow of the inhaling person Q

_{b,in}; and fourth, the total filter efficiency of the face masks considered by the filter factor f

_{M}.

- Virus-related factor (VF)

_{V}can therefore be described as the product of the particle emission rate N

_{p}, a factor considering their size distribution f

_{p}and the viral load n

_{v}(see Equation (18)).

_{p}describes a conversion factor from the particle emission rate per second to their volume emission rate per hour and depends on the size distribution. In the following calculations, a value of ${\mathrm{f}}_{\mathrm{P}}=1.1523\times {10}^{8}\frac{\mathrm{mL}\xb7\mathrm{s}}{\mathrm{P}\xb7\mathrm{h}}$ is used. The calculation of this conversion factor is displayed in the Appendix A.

_{0}is assumed to be in the range of 100 to 300 viral copies [25]. The virus-related factor is defined in Equation (17).

- 2
- Situation-related factor (SF)

_{R}, the overall lambda (λ

_{g}) and the time of stay (t). In a steady state it can therefore easily be derived from Equation (12) and will result in Equation (19). For an unsteady situation, the equation for the concentration (see Figure 1 and Equation (20)) has to be integrated to obtain Equation (21).

- 3
- Susceptible-person-related factor (SPF)

_{b,ex}) of the infected person and the inhalation flow rate (Q

_{b,in}) of the susceptible persons. To calculate the number of inhaled particles, just the inhaled volume flow rate (Q

_{b,in}) has to be considered.

- 4
- Personal-protection-measures-related factor (PPF)

_{m,e}as well as f

_{m,in}is the ratio of particles going by the mask, or the difference between 1 and the ratio of particles separated by the mask.

_{s}, the following assumptions must be considered:

- The aerosol is ideally mixed in the room.
- The near field can contain a much higher virus-laden particle concentration, but it is neglected in the following.
- The air, which is introduced into the room, is free of virus-laden particles.
- A constant decay rate of deposition occurs (in this consideration ${\mathsf{\lambda}}_{\mathrm{sed}}=0.2\frac{1}{\mathrm{h}}$)
- A constant decay rate because of inactivation occurs (in this investigation ${\mathsf{\lambda}}_{\mathrm{in}}=0.6\frac{1}{\mathrm{h}}$)
- The concentration of virus-laden particles at the beginning of unsteady cases is 0 virus-laden particles/m
^{3}.

## 3. Results

_{R}(steady (regarding Equation (19)) and unsteady (regarding Equation (21))), f

_{M}and O

_{b,in}can also be seen in Table 1.

_{0}is assumed to be the minimal value of 100 viral copies, and in Figure 4 a higher value of 300 viral copies, both related to [25]. With a higher critical dose, the lines with similar PAR

_{s}are shifted upwards, whereas either a higher viral load or a higher particle emission rate is necessary to result in the same PAR

_{s}. It can be seen that the viral load for all investigated outbreaks had to be higher than 10

^{8}viral copies/mL to explain the outbreaks with the given boundary conditions. If instead of Equation (21) for the time-dependent calculation, Equation (19) for the steady-state assumption is used, the values ${\frac{{\mathrm{S}}_{\mathrm{v}}}{{\mathrm{N}}_{0}}}_{\mathrm{steady}}$ are lower than the values calculated for the unsteady conditions. Nevertheless, the viral load had to be higher than 10

^{8}viral copies/mL to reach the ARs (see Table 1).

_{v}/N

_{0}were calculated. For lower attack rates (French Choir, D) or less singing (Berlin 2, B), the emission rate was calculated to be lower and in the same range as for the call center I, the fitness classes (F, G) or the slaughterhouse (H). Furthermore, the outbreak in the restaurant (K), the minivan 1 (P) and the club meeting (R) revealed high values for the inhaled number of infectious particles compared with the critical dose. A possible explanation is that in these situations the infectious person talked louder, because other persons talked as well or the infectious person had a higher viral emission.

_{v}/N

_{0}ranged between 100 and 700 1/h, which is lower than for the choir or meeting outbreaks, but higher than for the other outbreaks correlated with public transport (L, M, N, O, Q).

#### 3.1. Derivation of Simplified Key Figures and Calculations for the Assessment of Infection Risks and Preventive Measures

_{S}is defined as the situational reproduction number (the number of persons probably infected during the situation), which should be statistically valid.

_{R,s}can therefore be replaced by Equation (19).

_{Pers}as the specific volume flow (person-related volume flow) in m

^{3}per hour and person.

_{S}= 1, so no outbreak would probably happen due to aerosol transmission (definition of outbreak: more than one person becoming infected during a transmission event). In rooms with a number of susceptible persons ${\mathrm{N}}_{\mathrm{Pers}}\gg \mathrm{I}$, $\mathrm{ln}\left(1-\frac{1}{{\mathrm{N}}_{\mathrm{Pers}}}\right)\approx \frac{1}{{\mathrm{N}}_{\mathrm{Pers}}}$ and $\frac{\left({\mathrm{N}}_{\mathrm{Pers}}+\mathrm{I}\right)}{{\mathrm{N}}_{\mathrm{Pers}}}\cong 1$ will result in a small error compared to the origin and Equation (29) can be simplified into Equation (30).

_{S}= 1.

_{2}concentration. Whereas the number of inhaled particles increases linearly with time of stay (in case of steady state), the CO

_{2}concentration does not change, and caution has to be taken when using the CO

_{2}concentration as an indicator for a risk of infection.

_{b,in}= 0.54 m

^{3}/h (low activity (breathing while sitting, standing or talking)). In Figure 5, the specific volume flow per person and hours of stay necessary to infect not more than one further person are displayed.

_{S}≤ 1), whereas a much higher air supply is necessary. The volume flows in the red area cannot be reached in rooms with common airflow rates.

_{Pers}, a specific volume per person (V

_{Pers}) can be used together with the overall lambda (λ

_{g}) to convert Equation (31) into Equation (33).

_{s}according to Equation (35) as well as R

_{s}according to Equation (36) can be predicted relatively well within the limited range of values.

_{r}can be defined according to Equation (37). If the VF remains the same in the rooms being compared (identical virus variant), then the risk factor depends on SF, SPF, and PPF only.

#### 3.2. Influence of Variants of Concern (VOC)

_{v}/N

_{0}ratio to the PAR

_{s}is shown in Figure 7.

#### 3.3. Comparison of Prevention Measures: Ag Testing, Wearing Masks, and Increasing Ventilation Rate

_{v}/N

_{0}) is dominant in PAR

_{S}. S

_{v}/N

_{0}varies by a factor of 1000 between a viral load of 10

^{8}and 10

^{11}. The preventive measures (increasing the virus-free air supply volume, wearing masks, reducing the time of stay and their combination) in the specific situation have to be of a similar order of magnitude to actually prevent an outbreak. The comparison was performed with the simplified model, which is valid for lower PAR

_{s}, and in the case of high PAR

_{s}further measures should be implemented, so that the actual value for higher PAR

_{s}is not relevant. If the lower limit of the supplied virus-free air volume flow is calculated to reach a CO

_{2}concentration of 4000 ppm (common for not regularly performed window ventilation and longer stays) and the volume flow is increased until a lowered CO

_{2}concentration of 1000 ppm is reached (complies with the normative recommendation for indoor air quality), the factor of change is 7 related to the air volume flow and the preventive impact. Wearing a face mask, on average, reduces the inhaled dose by 50%, whereas a factor of 2 can also be applied for halving the time of stay in the room together with the infectious person. For a FFP2 mask the dose will, on average, be reduced by 80%, whereas a factor of 5 can be applied.

^{8}to 10

^{9}, could probably be compensated for by wearing masks and ventilating regularly (Figure 10, blue bar: face mask + 1000 ppm). If the virus source entering the room can be avoided, it is obvious that this is the most effective preventive measure. Ag tests can be of practical use, even if their sensitivity is limited for low and medium viral load.

## 4. Discussion

^{3}and a supply of virus-free air. An ideal mixing of all particles in the room also implies that no separation into the near and far field can be performed, whereas the concentration of virus-laden particles near the person is probably higher than in the rest of the room. Additionally, the local concentration will differ regularly from the average concentration, such that the local air quality index should be considered for investigation in detail [28,29]. As a result, even at lower viral emission rate, S

_{v}, infection can occur via aerosol, predominantly in the near field. As a third aspect, the influence of VOCs is difficult to define. A higher transmission rate of new VOCs may result from different aspects, such as a change in critical dose, a change in viral load or a change in other measures. It also has to be kept in mind that the investigated outbreaks documented with ARs from 4% to 100% had mostly high ARs and therefore resulted in a high number of newly infected persons. Many transmission events have much lower ARs, so the results may over- or understate the true risk.

^{8}viral copies/mL, aerosol transmission becomes unlikely if the distance is maintained. However, it has to be considered that in some of the investigated cases, the range between the 25% and the 75% percentile is quite high, which is because of insecure boundary conditions.

## 5. Conclusions

- (1)
- For an outbreak due to aerosol transmission to happen, high viral loads are required, which regularly occurs with the Delta variant.
- (2)
- Preventive measures such as wearing masks and rising ventilation cannot prevent an outbreak when virus loads are very high, but are useful to mitigate it.
- (3)
- The person-related air flow rate per hour of stay is a favorable indicator for evaluating the preventive effect of ventilation measures. According to our observations, even volume flow rate and person-related volume flow rate have a more informative quality than the air change rate.
- (4)
- Instead of CO
_{2}concentration, the CO_{2}dose (integration of the difference from the outdoor air concentration) is suitable for defining a limit value that should not be exceeded. - (5)
- With a simplified approach it is easy to compare different indoor situations and preventive measures regarding aerosol transmission.
- (6)
- Ag tests possess an effective additional quality: they have a high sensitivity (detection rate) at virus loads of more than 10
^{6}viral copies/mL and are therefore able to detect infectious persons, providing the chance to isolate them before entering a room for a longer stay.

^{8}(viral copies)/mL was necessary to reach the observed attack rates. This demonstrates that the viral load estimated from the swab might overestimate a person’s infectivity via aerosol, because a person is generally considered infectious, independent of the transmission method, when the viral load from the swab is 10

^{6}viral copies/mL. It can be seen that the viral emission of the infected person is the dominant influencing factor, but three further aspects (situational aspects, personal aspects of the susceptible persons and preventive measures) have to be considered to transfer a transmission of SARS-CoV-2 into a superspreading event. It can be concluded that higher activity (such as singing or physical activity) alone does not necessarily result in high ARs (Choir Rehearsal Berlin 2) and that lower activity may also result in high ARs (e.g., School Hamburg 1) if other unfavorable conditions (e.g., high viral load, ineffective preventive measures) occur.

_{2}concentration in the room, but whereas the number of inhaled virus-laden particles increases with time, the CO

_{2}concentration will reach a steady-state concentration after a certain time, and does not change much until the persons leave the room. In comparison, the number of inhaled virus-laden particles increases over time even if their concentration in the room stays constant. Therefore, to use a fixed CO

_{2}concentration as an indicator for the risk of infection has important limitations. Instead, the CO

_{2}dose ($\mathrm{ppm}\xb7\mathrm{h}$) can be used meaningfully and is easy to integrate in an infection risk monitoring system.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Appendix A

#### Calculation of the Conversion Factor from Number to Volume of the Particles

Particle Emission Rate in Particles/s | |||||||
---|---|---|---|---|---|---|---|

Cumulative | 0.3–0.5 µm | 0.5–1.0 µm | 1.0–3.0 µm | >3.0 µm | |||

Adults [35,35,39] | Breathing through the nose (26 subjects) | Average | 32 | 17 | 9 | 5 | 0 |

Median | 16 | 12 | 4 | 2 | 0 | ||

Min | 0 | 0 | 0 | 0 | 0 | ||

Max | 740 | 314 | 262 | 159 | 12 | ||

Breathing through the mouth (37 subjects) | Average | 164 | 87 | 48 | 27 | 1 | |

Median | 68 | 36 | 16 | 10 | 0 | ||

Min | 2 | 0 | 0 | 0 | 0 | ||

Max | 1036 | 612 | 381 | 148 | 18 | ||

Speaking (45 subjects) | Average | 268 | 152 | 77 | 38 | 1 | |

Median | 212 | 118 | 49 | 24 | 0 | ||

Min | 17 | 4 | 0 | 0 | 0 | ||

Max | 1194 | 730 | 330 | 275 | 25 | ||

Coughing * (7 subjects) | Average | 13,708 | 8047 | 3478 | 2057 | 126 | |

Median | 9790 | 6494 | 2806 | 2315 | 98 | ||

Min | 1805 | 1099 | 392 | 314 | 0 | ||

Max | 287,697 | 196,781 | 71,826 | 18,933 | 353 | ||

Singing (39 subjects) | Average | 1511 | 842 | 458 | 208 | 2 | |

Median | 1376 | 742 | 396 | 166 | 0 | ||

Min | 133 | 72 | 31 | 28 | 0 | ||

Max | 6215 | 3677 | 1989 | 1457 | 23 | ||

Shouting (15 subjects) | Average | 1843 | 1105 | 507 | 231 | 0 | |

Median | 1295 | 777 | 353 | 165 | 0 | ||

Min | 330 | 141 | 94 | 71 | 0 | ||

Max | 5862 | 3743 | 1719 | 471 | 0 | ||

Adolescents (13–15 years) [38] | Breathing (7 subjects) | Average | 54 | 18 | 16 | 19 | 1 |

Median | 41 | 17 | 5 | 14 | 0 | ||

Min | 0 | 0 | 0 | 0 | 0 | ||

Max | 749 | 352 | 201 | 179 | 17 | ||

Speaking (8 subjects) | Average | 112 | 65 | 25 | 20 | 3 | |

Median | 98 | 51 | 20 | 11 | 1 | ||

Min | 13 | 5 | 5 | 0 | 0 | ||

Max | 251 | 137 | 55 | 53 | 13 | ||

Singing (8 subjects) | Average | 577 | 284 | 166 | 122 | 5 | |

Median | 490 | 286 | 127 | 72 | 3 | ||

Min | 165 | 64 | 33 | 19 | 0 | ||

Max | 1229 | 529 | 337 | 345 | 17 | ||

Shouting (8 subjects) | Average | 2940 | 1491 | 820 | 603 | 26 | |

Median | 2477 | 1417 | 697 | 461 | 9 | ||

Min | 720 | 410 | 151 | 160 | 0 | ||

Max | 5048 | 2486 | 1464 | 1088 | 104 | ||

Children (8–10 years) [40] | Breathing (15 subjects) | Average | 2 | 2 | 0 | 0 | 0 |

Median | 0 | 0 | 0 | 0 | 0 | ||

Min | 0 | 0 | 0 | 0 | 0 | ||

Max | 23 | 23 | 0 | 0 | 0 | ||

Speaking (15 subjects) | Average | 40 | 27 | 3 | 8 | 2 | |

Median | 24 | 24 | 0 | 0 | 0 | ||

Min | 0 | 0 | 0 | 0 | 0 | ||

Max | 118 | 71 | 47 | 47 | 23 | ||

Singing (14 subjects) | Average | 131 | 72 | 34 | 25 | 0 | |

Median | 118 | 59 | 35 | 23 | 0 | ||

Min | 0 | 0 | 0 | 0 | 0 | ||

Max | 800 | 400 | 235 | 165 | 0 | ||

Shouting (15 subjects) | Average | 1166 | 614 | 298 | 250 | 5 | |

Median | 1012 | 589 | 259 | 188 | 0 | ||

Min | 23 | 23 | 0 | 0 | 0 | ||

Max | 2260 | 1177 | 659 | 659 | 47 |

_{i}the proportion of particles in the size class and V

_{i}the volume of particles in this size class.

## Appendix B

#### Necessary Boundary Conditions to Retrospectively Investigate Outbreaks

- (1)
- Virus-related aspects
- How many people were infected by the virus?
- How many people attended the event?
- How many people were vaccinated or had recovered from an infection?
- Has it been defined which type of virus caused the infection? If yes, which one?
- How high was the virus load during the infection event?

- (2)
- Room-related aspects
- How big is the room in which the event took place (area, volume)?
- Was the room ventilated mechanically?
- What volume flow or air change rate was available?

- Was the room ventilated by window opening?
- How often and for how long were the windows opened?
- Is there anything known about the outdoor conditions on that day? (Temperature, wind speed, wind direction.)

- (3)
- Event-related aspects
- How long did the event take?
- Did all attendees stay in the room together for the whole event? Otherwise, specify which part left and for how long.
- What was the main activity of the infectious person?
- What was the main activity of the susceptible persons?
- Were there any additional preventive measures (e.g., face masks)?
- Were the persons at fixed positions during the stay? What were the approximate positions of the persons?

## Appendix C

^{3}. The duration of the rehearsals differed just slightly, between 2 and 2.5 h.

^{3}). The bus travel lasted between 1 and 2.5 h.

_{M}= 0.7) and noted some symptoms, whereas he reduced speaking intensity.

Choir Rehearsal Berlin 1 | Choir Rehearsal Berlin 2 | Skagit Valley Choir | French Choir | Korean Call Center | Korean Fitness Center | Hawaiian Fitness Class | German Slaughterhouse | |
---|---|---|---|---|---|---|---|---|

Source/s | [40] | [40] | [30,31] | [74] | [31,77] | [31,78] | [75] | [76] |

Air change rate in 1/h | 0.17 | 0.45 | [31] 1.5, [30] 0.3–1.0 | unventilated, assumed 0.1 | [31] 1.5 | [31] 1.5 | unventilated, assumed 0.1 | 0.53 |

0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | ++ ±5% | |

Room volume in m^{3} | 1200 | 1720 | 810 | 135 | 1143 ** | 180 | 114 *** | 3000 |

++ ±5% | ++ ±5% | + ±20% | + ±20% | + ±20% | + ±20% | 0 ± 50% | + ±20% | |

Number of previously infected persons | 1 | 1 | 1 | 1 * | 1 | 1 | 1 | 1 |

++ ±5% | ++ ±5% | ++ ±5% | 0 ± 50% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | |

Number of susceptible persons | 77 | 42 | 61 | 25 | 89 | 192 | 10 | 78 |

Main activity | Singing | Singing/Speaking | Singing | Singing | Speaking | Physical Activity | Physical Activity | Heavy working |

Breathing volume flow (Q_{b,e} and Q_{b,in}) in m^{3}/h | 0.65 | 0.61 | 0.65 | 0.65 | 0.54 | 0.9 | 0.9 | 0.9 |

+ ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | |

Mask efficiency in % | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

- | - | - | - | - | - | - | - | |

Time of stay in h | 2.5 | 2 | 2.5 | 2 | 8 | 0.8 | 1 | 8 |

++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | + ±20% | ++ ±5% | ++ ±5% | + ±20% | |

Attack rate in % | 89 | 24 | 87 | 68 | 65 | 30 | 100 | 26 |

++ ±5% | ++ ±5% | + ±20% | + ±20% | ++ ±5% | + ±20% | + ±20% | ++ ±5% |

^{3}. *** Area given, height of 3 m assumed.

School Israel | Courtroom | Wuhan Restaurant | Aircraft | Buddhist Bus | Wuhan (Bus 1) | Wuhan (Bus 2) | Minivan 1 | Minivan 2 | |
---|---|---|---|---|---|---|---|---|---|

Source/s | [79] | [80] | [1,85] | [81] | [31,82] | [31,83] | [31,83] | [84] | [84] |

Air change rate in 1/h | 2.7 | unknown, assumed 0.3 | [1] 0.56–0.77 | 21 | 3 | 3 | 3 | 9 | 9 |

0 ± 50% | 0 ± 50% | 0 ± 50% | + ±20% | 0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | |

Room volume in m^{3} | 150 | 150 | [19] 431 * | 60 ** | 50 | 71 | 34 | 16 | 16 |

++ ±5% | ++ ±5% | + ±20% | ++ ±5% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | |

Number of previously infected persons | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | |

Number of susceptible persons | 66 | 9 | 21 | 19 | 68 | 48 | 12, 1 with mask | 4, all with cloth masks | 3, infected person w/o mask, other persons w/mask |

Main activity | Speaking | Speaking | Speaking | Speaking | Speaking | Speaking | Speaking | Speaking | Speaking |

Breathing volume flow (Q_{b,e} and Q_{b,in}) in m^{3}/h | 0.5 | 0.54 | 0.54 | 0.54 | 0.54 | 0.54 | 0.54 | 0.54 | 0.54 |

+ ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | |

Mask efficiency in % | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.7 | 0.85 |

- | - | - | - | - | - | - | + ±20% | + ±20% | |

Time of stay in h | 4.5 | 3 | 1.2 | 11 | 1.7 | 2.5 | 1.0 | 2 | 2 |

++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | |

Attack Rate in % | 43 | 33 | 45 | 6 | 34 | 15 | 17 | 100 | 33 |

++ ±5% | + ±20% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% |

^{3}. ** Only the Business Class is included where the majority of infections occurred. Evaluation of the security of the boundary conditions ++ quite secure, + somewhat insecure, 0 unknown/insecure, assumed level of deviation.

Club Meeting | School Berlin 1 | School Berlin 2 | Meeting Germany | School Hamburg 1 | School Hamburg 2 | School Hamburg 3 | School Hamburg 4 | |
---|---|---|---|---|---|---|---|---|

Source/s | [86] | [86] | [86] | [86] | [87] | [87] | [87] | [87] |

Air change rate in 1/h | 0.20 | 8.3 | 10 | 1.2 | 1.9 | 3.3 | 3.2 | 3.2 |

0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | 0 ± 50% | |

Room volume in m^{3} | 254 | 180 | 150 | 170 | 154 | 157 | 157 | 157 |

++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | |

Number of previously infected persons | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | |

Number of susceptible persons | 25 | 27 | 20 | 11 | 28 | 24 | 24 | 27 |

Main activity | Speaking | Speaking | Speaking | Speaking | Speaking | Speaking | Speaking | Speaking |

Breathing volume flow (Q_{b,e} and Q_{b,in}) in m^{3}/h | 0.54 | 0.45 | 0.45 | 0.54 | 0.54/0.45 * | 0.54/0.45 * | 0.54/0.45 * | 0.54/0.45 * |

+ ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | + ±20% | |

Mask efficiency in % | 1 | 1 | 1 | 1 | 1 | 1 | 0.7 | 0.7 |

- | - | - | - | - | - | + ±20% | + ±20% | |

Time of stay in h | 1.5 | 4.5 | 1.5 | 2 | 3 | 1.5 | 1.5 | 0.75 |

++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | |

Attack rate in % | 58 | 10 | 6 | 17 | 57 | 33 | 13 | 4 |

++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% | ++ ±5% |

## Appendix D

#### Comparison of Different Situations

^{10}viral copies/mL was used. For the situation in the supermarket with mask, which is currently common, R

_{s}= 1 is used as the reference. In all situations, the duration of stay is longer than in the supermarket, but in the theater/cinema scenario the risk is lower than in the supermarket. In all other situations the risk is higher, and if the duration of stay is much longer (office or school) the risk is significantly higher and further measures (reduction in the number of persons in the room, wearing masks) are necessary to reduce the risk.

N_{p} in P/s | S_{v}/N_{0} in Viral Copies/h | t in h | q_{pers} in m^{3}/h×Per | Q_{b,in} in m^{3}/h | f_{M} in - | R_{s} in Per | x_{r} in - | |
---|---|---|---|---|---|---|---|---|

Reference: supermarket, with mask | 160 | 184 | 0.5 | 25 | 0.54 | 0.5 | 1 | 1 |

Office half occupancy, without mask | 160 | 184 | 8 | 60 | 0.54 | 1 | 13.2 | 13.2 |

Office half occupancy, with mask | 160 | 184 | 8 | 60 | 0.54 | 0.5 | 6.6 | 6.6 |

School normal occupancy, without mask | 80 | 92 | 6 | 25 | 0.54 | 1 | 11.9 | 11.9 |

School half occupancy, without mask | 80 | 92 | 6 | 50 | 0.54 | 1 | 6 | 6 |

School half occupancy, with mask | 80 | 92 | 6 | 50 | 0.54 | 0.5 | 3 | 3 |

Restaurant normal occupancy | 160 | 184 | 1.5 | 50 | 0.54 | 1 | 6 | 6 |

Restaurant half occupancy | 160 | 184 | 1.5 | 100 | 0.54 | 1 | 3 | 3 |

Theater/cinema half occupancy, with mask | 80 | 92 | 2 | 60 | 0.54 | 0.5 | 0.8 | 0.8 |

_{p}—particle emission rate. $\frac{{\mathrm{S}}_{\mathrm{v}}}{{\mathrm{N}}_{0}}$—virus emission rate of the infectious person divided by the critical dose. t, time of stay. q

_{pers}—specific volume flow per person. Q

_{b,in}—inhalation flow rate of the susceptible persons. f

_{M}—mask efficiency considering the inhalation and exhalation efficiency. R

_{s}—number of newly infected persons in a specific situation. x

_{r}—risk factor for a specific situation.

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**Figure 1.**Relative concentration curve as a function of air change rate and time, based on the steady-state concentration.

**Figure 3.**Virus factor (VF) for different viral loads and particle emission rates with N

_{0}= 100 viral copies. The attack rates found in the investigated outbreaks are shown with the different colors; the markers show the amount of virus factor at assumed mean particle emission rate of the related activity according to Figure 2.

**Figure 4.**Virus factor (VF) for different viral loads and particle emission rates with N

_{0}= 300 viral copies. The attack rates found in the investigated outbreaks are shown with the different colors; the markers show the amount of virus factor at assumed mean particle emission rate of the related activity according to Figure 2.

**Figure 5.**Specific volume flow depending on the number of emitted particles and the viral load to limit the number of newly infected persons to one; N

_{0}= 100 viral copies, f

_{M}= 1, Q

_{b,in}= Q

_{b,ex}= 0.54 m

^{3}/h.

**Figure 6.**Comparison of the risk factor x

_{r}for different everyday life situations with a 0.5 h stay in a supermarket, wearing a mask as reference.

**Figure 7.**Virus factor for different viral loads and critical doses with a particle emission rate of 100 P/s, (

**left**) and 1000 P/s (

**right**); the attack rates found in the investigated outbreaks are shown with different colors.

**Figure 8.**Viral emission for different viral loads and particle emission rates with N

_{0}= 67 viral copies; the attack rates found in the investigated outbreaks are shown with different colors.

**Figure 9.**Specific volume flow depending on the number of emitted, particles and the viral load to limit the number of newly infected persons to one; N

_{0}= 67 viral copies, f

_{M}= 1, Q

_{b,in}= Q

_{b,e}= 0.54 m

^{3}/h.

**Figure 10.**Influence of different preventive measures on the risk of an outbreak. The red bar represents the viral load and the resulting risk factor (Equation (37)). The blue bars illustrate different combinations of preventive measures in the form of a risk reduction factor (also according to Equation (37)).

AR in % | Situation-Related Factor (SF) | $\mathbf{Susceptible}-\mathbf{Person}-\mathbf{Related}\mathbf{Factor}\left(\mathbf{SPF}\right){\mathbf{Q}}_{\mathbf{b},\mathbf{in}}\mathbf{in}\frac{\mathbf{m}3}{\mathbf{h}}$ | Personal-Protection-Measures-Related Factor (SPF) f_{M} | Virus-Related Factor (VF) | $\frac{{\mathbf{S}}_{\mathbf{v}}}{{\mathbf{N}}_{0}}$$\mathbf{in}\frac{1}{\mathbf{h}}(\mathbf{Monte}-\mathbf{Carlo}-\mathbf{Simulation})$ | |||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathbf{C}}_{\mathbf{R}}$$\mathbf{in}\frac{\mathbf{h}2}{\mathbf{m}3}$ | ${\mathbf{C}}_{\mathbf{R},\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{a}\mathbf{d}\mathbf{y}}$$\mathbf{in}\frac{\mathbf{h}2}{\mathbf{m}3}$ | $\frac{{\mathbf{S}}_{\mathbf{v}}}{{\mathbf{N}}_{0}}$$\mathbf{in}\frac{1}{\mathbf{h}}$ | ${\frac{{\mathbf{S}}_{\mathbf{v}}}{{\mathbf{N}}_{0}}}_{\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{a}\mathbf{d}\mathbf{y}}$$\mathbf{in}\frac{1}{\mathbf{h}}$ | Median | 25% Percentile | 75% Percentile | ||||

Choir Rehearsal Berlin 1 (A) | 89 | 0.0013 | 0.0022 | 0.65 | 1 | 2529 | 1576 | 2594 | 2145 | 3220 |

Choir Rehearsal Berlin 2 (B) | 24 | 0.006 | 0.0009 | 0.65 | 1 | 732 | 464 | 774 | 656 | 916 |

Skagit Valley Choir (C) | 87 | 0.0019 | 0.0030 | 0.65 | 1 | 1649 | 1065 | 1932 | 1226 | 3335 |

French Choir (D) | 68 | 0.0088 | 0.0165 | 0.65 | 1 | 199 | 107 | 200 | 144 | 281 |

Korean Call Center (E) | 12 | 0.0018 | 0.0018 | 0.54 | 1 | 135 | 133 | 345 | 254 | 462 |

Korean Fitness Center (F) | 30 | 0.0011 | 0.0019 | 0.9 | 1 | 378 | 205 | 375 | 283 | 495 |

Hawaiian Fitness Class (G) | 100 | 0.0033 | 0.0098 | 0.9 | 1 | 2312 | 787 | 1014 | 523 | 1686 |

German Slaughterhouse (H) | 26 | 0.0018 | 0.0020 | 0.9 | 1 | 185 | 167 | 184 | 150 | 226 |

School Israel (I) | 43 | 0.0052 | 0.0058 | 0.54 | 1 | 216 | 195 | 140 | 103 | 184 |

Courtroom (J) | 33 | 0.0115 | 0.0154 | 0.54 | 1 | 58 | 41 | 57 | 46 | 73 |

Wuhan Restaurant (K) | 45 | 0.0096 | 0.0192 | 0.54 | 1 | 115 | 58 | 120 | 97 | 149 |

Aircraft (L) | 62 | 0.0084 | 0.0084 | 0.54 | 1 | 214 | 213 | 212 | 173 | 261 |

Buddhist Bus (M) | 34 | 0.0076 | 0.0090 | 0.54 | 1 | 102 | 86 | 99 | 72 | 133 |

Wuhan (Bus 1) (N) | 15 | 0.0084 | 0.0094 | 0.54 | 1 | 36 | 32 | 35 | 25 | 48 |

Wuhan (Bus 2) (O) | 17 | 0.0058 | 0.0079 | 0.54 | 1 | 59 | 44 | 59 | 45 | 78 |

Minivan 1 (P) | 63 | 0.0124 | 0.0131 | 0.54 | 0.5 | 481 | 455 | 475 | 309 | 690 |

Minivan 2 (Q) | 45 | 0.0124 | 0.0131 | 0.54 | 0.7 | 85 | 81 | 83 | 54 | 121 |

Club Meeting (R) | 58 | 0.0029 | 0.0059 | 0.54 | 1 | 564 | 271 | 568 | 485 | 670 |

School Berlin 1 (S) | 10 | 0.0038 | 0.0039 | 0.45 | 1 | 56 | 54 | 87 | 59 | 118 |

School Berlin 2 (T) | 6 | 0.0015 | 0.0016 | 0.45 | 1 | 85 | 76 | 157 | 109 | 212 |

Meeting Germany (U) | 17 | 0.0045 | 0.0060 | 0.54 | 1 | 77 | 58 | 79 | 64 | 97 |

School Hamburg 1 (V) | 57 | 0.0062 | 0.0071 | 0.45 | 1 | 271 | 238 | 295 | 225 | 381 |

School Hamburg 2 (W) | 33 | 0.0020 | 0.0024 | 0.45 | 1 | 401 | 334 | 456 | 344 | 592 |

School Hamburg 3 (X) | 13 | 0.0020 | 0.0024 | 0.45 | 0.7 | 199 | 166 | 224 | 165 | 300 |

School Hamburg 4 (Y) | 4 | 0.0008 | 0.0012 | 0.45 | 0.7 | 143 | 97 | 161 | 123 | 210 |

Min | 4 | 0.0006 | 0.0009 | - | - | 36 | 32 | 35 | 25 | 48 |

Max | 89 | 0.0160 | 0.0012 | - | - | 2529 | 1576 | 2594 | 2145 | 3320 |

_{b,in}—inhalation flow rate of the susceptible persons. f

_{M}—mask efficiency considering the inhalation and exhalation efficiency. $\frac{{\mathrm{S}}_{\mathrm{v}}}{{\mathrm{N}}_{0}}$—virus emission rate of the infectious person divided by the critical dose. ${\frac{{\mathrm{S}}_{\mathrm{v}}}{{\mathrm{N}}_{0}}}_{\mathrm{steady}}$—virus emission rate of the infectious person divided by the critical dose in a steady situation.

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**MDPI and ACS Style**

Kriegel, M.; Hartmann, A.; Buchholz, U.; Seifried, J.; Baumgarte, S.; Gastmeier, P.
SARS-CoV-2 Aerosol Transmission Indoors: A Closer Look at Viral Load, Infectivity, the Effectiveness of Preventive Measures and a Simple Approach for Practical Recommendations. *Int. J. Environ. Res. Public Health* **2022**, *19*, 220.
https://doi.org/10.3390/ijerph19010220

**AMA Style**

Kriegel M, Hartmann A, Buchholz U, Seifried J, Baumgarte S, Gastmeier P.
SARS-CoV-2 Aerosol Transmission Indoors: A Closer Look at Viral Load, Infectivity, the Effectiveness of Preventive Measures and a Simple Approach for Practical Recommendations. *International Journal of Environmental Research and Public Health*. 2022; 19(1):220.
https://doi.org/10.3390/ijerph19010220

**Chicago/Turabian Style**

Kriegel, Martin, Anne Hartmann, Udo Buchholz, Janna Seifried, Sigrid Baumgarte, and Petra Gastmeier.
2022. "SARS-CoV-2 Aerosol Transmission Indoors: A Closer Look at Viral Load, Infectivity, the Effectiveness of Preventive Measures and a Simple Approach for Practical Recommendations" *International Journal of Environmental Research and Public Health* 19, no. 1: 220.
https://doi.org/10.3390/ijerph19010220