**6. Strategies against SARS-CoV-2 direct transmission within confined spaces**

The strategy to minimize the risk of virus spreading must avoid the viral load reaching the susceptible subject. Alternatively, any viral load that comes into contact with the host surface should be responsible for a negligible risk of infection, i.e., equal to or less than 10<sup>5</sup> virions/mL [9]. As for industrial practice where filtration processes are carried out in two stages, in an enclosed space where at least one infected subject and other susceptible occupants are present, the infection risk is minimized by adopting two filters. The first filter is the mask or any other barrier that physically blocks with sufficient effectiveness the larger droplets that are the droplets that, statistically, contain the greatest number of virions. **Figures 2** and **3** schematically represent, respectively, two subjects with and without the facial mask. Once emitted, droplets' trajectory toward the susceptible subjects depends on ambient air fluid dynamic and thermohygrometric conditions. Assuming the experimental data of [12], an infected subject who does not wear a mask emits during a conversation, on

*Perspective Chapter: Analysis of SARS-CoV-2 Indirect Spreading Routes and Possible… DOI: http://dx.doi.org/10.5772/intechopen.105914*

#### **Figure 2.**

*Direct transmission occurring between infected and susceptible subjects that do not wear a mask or other physical barrier.*

#### **Figure 3.**

*Direct transmission occurring between infected and susceptible subjects that wear a mask or other physical barrier.*

average, 460 droplets per minute whose size distribution is reported in **Figure 4**. In the worst case, the number of emitted droplets can be up to approximately 1850 per minute. On the other hand, conservatively, wearing a mask not all the droplets are captured, and vice versa, some of them escape due to the imperfect seal on the face [27]. Since no confirmation about the size of escaping particles is currently available, conservatively assuming a diameter less than or equal to 30 microns, for example, the rate of emitted droplets is about 10 times lower than the previous case. If higher tightness is achieved, a lower emission rate would be possible. For example, if the mask would block all the droplets with a diameter greater than 20 microns, the emission rate would be reduced by a factor of 30.

According to the shown data, coughing without a mask, almost 110 droplets per cough are emitted. Wearing a facial mask, the emission rate is reduced at least by a

**Figure 4.** *Droplet rate emission during a conversation.*

factor of 10. The role of the mask is even more evident considering the number of virions emitted in the environment. **Figure 5** shows that more than 87% of virions are emitted during speech within droplets having a diameter greater than 450 microns, i.e., 5% of the total emitted droplets. Therefore, assuming conservatively a threshold value of 30 microns (9% of the total emitted droplets), the droplets that can escape the facial mask during a speech carry, on average, about 0.0024% of the total virions. The same is for coughing. Better results would be achieved by tight facial masks. For example, let us assume a viral load at the emission equal to 1010.42 virions/mL. This value is the upper limit found in SARS-CoV-2 positive samples, and it refers to SARS-CoV-2 infection in the early stages of the COVID-19 pandemic [28]. If the same viral load characterizes all the droplets at the emission, the average virions emission rate is approximately 10 million virions per minute when no mask is worn. This value can achieve up to 45 million virions per minute for those infected subjects that emit more than the average, such as superemitters. Coughing without a mask, up to 58 million virions can be emitted per cough. Wearing a mask able to block droplets larger than 30 microns, the virions' emission rate can be reduced by a factor of 1000 or 50,000, respectively in the case of speech and cough.

Although the mask acts as the first element for reducing the risk of transmission of the infection, the infected droplets that escape are still a potential risk for susceptible individuals in the vicinity of an infected subject. Therefore, the second stage of filtration aims to minimize the infection risk occurring if the virion reaches the target negligible. The second barrier is immaterial and consists of the control of the air relative humidity and keeping a safe distance.

The safe distance is defined as the distance beyond which all the droplets have completely evaporated. The hypothesis is that all the carried virions are released into the surrounding ambient air and maintain their infectious potential. Therefore, droplet transmission is switched to airborne transmission. On the other hand, in the case of *Perspective Chapter: Analysis of SARS-CoV-2 Indirect Spreading Routes and Possible… DOI: http://dx.doi.org/10.5772/intechopen.105914*

#### **Figure 5.**

*Cumulative curves of the number of droplets (solid curve) and virions (dashed curve) during speech (blue) and cough (red).*

#### **Figure 6.**

*Simplified scheme to investigate droplets' motion toward a susceptible target.*

incomplete evaporation, the droplets reach the host surface at a viral load higher than the one they had at the emission. **Figure 6** shows infected and susceptible subjects, both equipped with masks. As the horizontal distance from the point of emission increases, the viral load of the infected droplets increases up to a maximum value calculated in Eq. (11). Regarding the scheme proposed in **Figures 6** and **7** shows the viral load of the droplets that come out of the mask with an initial diameter of 10

#### **Figure 7.**

*The trend of the viral load through the horizontal distance from the infected subject. The continuous and dashed curves were calculated for 50% and 70% relative humidity, respectively.*

microns, 20 microns, and 30 microns. The continuous curves refer to an air relative humidity equal to 50%, while the dashed ones refer to 70%. As the relative humidity increases, the front of the potential infection moves toward the susceptible subject. For example, the 30-micron droplets completely evaporate at 1.7 m for a relative humidity of 50%, while 2.2 m are necessary for a relative humidity of 70%. Therefore, at a distance of 1.8 m, an infected 30-micron droplet still conveys infecting particles with an air relative humidity of 70%.

**Figure 8** shows in the ordinate axis the infection probability of the host surface when a 30-micron droplet deposits its viral load on it. The distance is shown on the abscissa axis. Two initial viral loads are examined: 10<sup>5</sup> virions/mL and 10<sup>8</sup> virions/mL, i.e., one thousand times greater. The second case simulates a variant of the original SARS-CoV-2 virus that causes a greater average viral load at emission [29]. Although an initial viral load equal to 10<sup>5</sup> virions/mL is responsible for a negligible viral replication probability, when air relative humidity is equal to 70%, the evaporation causes the increase of the viral load and so the infection probability. In the case of a higher viral load at the emission, the role of relative humidity concerning the risk of viral infection is even more evident. To control the relative humidity at 50% would guarantee the blockage of the infection front at a distance of almost 1.8 m from the infected subject. On the other hand, with increasing air relative humidity up to 70%, the 30-micron droplet completely evaporates at a distance of 2.2 m; furthermore, a viral load able to infect still exists between 1.8 and 2.2 m. Therefore, without the air relative humidity control, the infection front moves toward or away from the susceptible subject based on the existing environmental thermohygrometric conditions.

*Perspective Chapter: Analysis of SARS-CoV-2 Indirect Spreading Routes and Possible… DOI: http://dx.doi.org/10.5772/intechopen.105914*

#### **Figure 8.**

*Estimation of cell culture replication probability through horizontal distance. Initial viral load equal 10<sup>8</sup> virions/ mL and 10<sup>5</sup> virions/mL are shown in red and blue, respectively. The continuous and dashed curves are calculated for 50% and 70% relative humidity, respectively.*

Virions are released into the air when droplets completely evaporate. Since the virion's average size is 100 nm, Brownian motion occurs. Once released, the virions are wetted particles. However, the liquid film evaporates quickly since the ratio between the evaporating surface and the mass of water is high. In the specific case, since the mass of water does not fill the entire volume but only the external layer of the virions, airborne transmission occurs after the evaporation of the aqueous film. The authors conservatively assume that the minimum volume of air where the virions are released is equal to the volume of exhaled air. In the case of speech, it is 11.7 L/min [26]. Assuming two subjects, one of which is infected, who speak together, if all the droplets that escape the mask evaporate before reaching the host surfaces, the viral load in the volume is, on average, equal to 2.6 <sup>10</sup><sup>6</sup> and 2.9 <sup>10</sup><sup>3</sup> virions/mL, respectively, for an initial viral load of 10<sup>5</sup> and 10<sup>8</sup> virions/mL.

Based on these viral loads and the Brownian motion of the virions, airborne transmission causes a negligible infection risk. **Figure 9** shows that the virions that can reach the host surface are those inside the control volume highlighted in red, whose height is equal to the diameter of the virion (indicated as *dz*). Therefore, the probability of infection with the airborne transmission is much lower than for droplet one. In droplet transmission, infected droplets are blocked by the target surface through interception or impact mechanisms, thus determining a significant deposition of virions in terms of both number and load. For simplicity, it can be assumed that the target surface has a size equivalent to the cross section of the droplets, as shown schematically in **Figure 10**.

#### **Figure 9.**

*The control volume where are located the virions that can touch the host surface is colored in red.*

**Figure 10.**

*Comparison between droplet transmission and airborne transmission.*

To compare the airborne and droplet transmissions, the number of the infected droplets that have to evaporate to be equivalent to a single infected droplet that reaches the host surface before evaporating is calculated. **Figure 11** shows the results for a 10-micron droplet. The infected subject should emit 1.2 <sup>10</sup><sup>14</sup> droplets so that the number of virions that reach the host through airborne transmission is equivalent to the number released on the same surface by a 10-micron droplet. Assuming the worst case for the speech, i.e., an emission rate equal to 1850 drops per minute, it would take 6.5 <sup>10</sup><sup>10</sup> min for the infected subject to emit that number of drops, or a time interval several orders of magnitude longer than what, reasonably, two individuals employed to speech.

#### **7. Conclusions**

This chapter demonstrates that available knowledge is largely inadequate to make predictions on the reach of infectious droplets emitted during an emission *Perspective Chapter: Analysis of SARS-CoV-2 Indirect Spreading Routes and Possible… DOI: http://dx.doi.org/10.5772/intechopen.105914*

**Figure 11.**

*Number of droplets that the infected subject must emit since the airborne transmission is equivalent to the droplet transmission of an infected droplet with a diameter between 1 and 30 microns.*

phenomenon since several research questions still need to be properly addressed: i) standardized characterization of the sizes and distribution of the exhaled droplets for all the human expulsion processes; ii) definition of the initial viral load of emitted droplets and the relationship with the viral load present in oronasopharyngeal swabs; iii) the effect the virions can induce on the droplet evaporation process; and iv) what happens to viruses after complete droplet evaporation and if they retain their full potential for infection.

Nevertheless, in this chapter, some hypotheses have been described to model and compare different SARS-CoV-2 spreading routes. The results show that an effective preventive strategy against SARS-CoV-2 spread cannot neglect three elements: using the facial mask, controlling the relative humidity, and keeping social distance. Particularly, the control of air relative humidity in confined spaces is an essential element. The time an infected droplet takes to evaporate completely depends on the relative humidity of the ambient air. The droplet can move in suspension or settle on a surface, but it remains a potential danger until it completely evaporates. In this case, droplet transmission is substituted by airborne transmission, which should be associated with a modest risk of contagion. The use of the mask allows for blocking of the larger droplets; the control of the air relative humidity guarantees, as suggested in this chapter, that the escaping droplets evaporate until a defined time before reaching the susceptible target. On the other hand, the social distance concept loses its effectiveness. If there is high humidity in the environment, the droplets that escape the mask and that do not settle on the ground would remain in suspension without evaporating and for a relatively long time, significantly increasing the probability of infection [30]. In the worst case, i.e., in saturation conditions (relative humidity equal to 100%), evaporation time tends to infinity, making the concept of safe distance meaningless: at no point in the confined environment, it would be possible to guarantee the absence of virion-carrying droplets. Particular attention must be paid to avoid a susceptible

individual coming into contact with droplets that have not completely evaporated. In such a case, cells' infection risk increases as the droplets' viral load is greater than the initial one. The contact with not completely evaporated droplets could explain, in the case of variants such as, for example, the delta variant, characterized by an average emission load higher by a factor of 10<sup>3</sup> than those of the original virus [29], the greater transmissibility. As the results show, the higher load at the emission determines an increase in the probability of infection of the susceptible targets' cells, especially in the case of high relative humidity conditions when the infection front moves forward. Although there are still many points to be clarified about virus transmission, only through the combined control of the air relative humidity, the social distance, and the wearing of the facial mask, it will be possible to ensure safe conditions in confined places and to minimize infection cases.
