**2. Size distribution of the infected droplets and calculation of the number of virions emitted**

Many studies are available in the literature focusing on analyzing the dimensional distribution of the droplets emitted for different possible emission mechanisms such as breathing, speech, cough, and sneezing. However, since no universally accepted standard test identifies the instrumentation and the procedure to investigate the topic, the results are difficult to compare with each other. For example, if a single cough event is considered, [10] states that the droplets in the submicron range represent 97% of the exhaled droplets, while [11] reports only less than 4% and [5] measures not even a single droplet within submicron range. Therefore, the first unsolved research question RQ1 is the standardized characterization of the sizes and the distribution of the exhaled droplets for all the expulsion processes.

Since a standard characterization of the initial distribution of droplet sizes is missing, in the following evaluation, the data reported by [12] were used. [12] has been selected as a data source due to the high number of citations, the robust methodology adopted, and the quality of exposure. The following results are affected by the data source selected; nevertheless, the focus of this chapter is more on the suggested methodology to assess SARS-CoV-2 spreading mechanisms and the related comparison. In [12], only droplets with a diameter greater than 20 microns were considered, although a "*16-channel dust monitor*" was available. Furthermore, only speech and cough mechanisms were investigated. In the first case, the involved subjects were asked to count from 1 to 100. Therefore, assuming that about 100 seconds are necessary to complete the count, the emission rate is calculated by dividing the droplets counted by this time interval. Moreover, the individuals were asked to make 20 coughs each to simulate the cough mechanism.

Since the data refer to a group of people, the average number of droplets *N*droplet,<sup>μ</sup> emitted by a subject for each *j*th-dimensional interval [drops/individual] is calculated as

$$N\_{\text{droplet},j,\mu} = \frac{\sum\_{i=1}^{N} N\_{\text{droplet},j,i}}{N\_{\text{sample}}} \tag{1}$$

where *N*droplet,*<sup>i</sup>* is the number of droplets emitted by the *i*th individual [droplets/ person], while *N*sample is the number of people who participated in the test. The number of droplets emitted by 99% of individuals, assuming a Gaussian distribution with a standard deviation σ*j*, for the *j*th interval is equal to

$$N\_{\text{droplet},j,99\%} = N\_{\text{droplet},j,\mu} + 2.58 \ast \sigma\_j \tag{2}$$

The total number of droplets emitted *N*droplet,<sup>μ</sup> and *N*droplet,99% are, respectively, computed as

$$N\_{\text{droplet},\mu} = \sum\_{j=1}^{M} N\_{\text{droplet},j,\mu} \tag{3}$$

$$N\_{\text{droplet},99\%} = \sum\_{j=1}^{M} N\_{\text{droplet},j,99\%} \tag{4}$$

where *M* is the number of dimensional intervals on which the range has been divided.

The definition of the initial viral load of emitted droplets and the relationship with the viral load present in oronasopharyngeal (ONP) swabs represents the second RQ2. To calculate the number of virions emitted, it was assumed that all the infected droplets had the same initial viral load λ<sup>0</sup> [RNA copies/mL]. This simplifying hypothesis is necessary since the topic is still under investigation and without clear results [13]. There is evidence that viral load in emitted droplets should be lower than in ONP swabs: for example, [14] detected RNA copies of SARS-CoV-2 in exhaled breaths (EBs), which was three to four orders of magnitude lower than the RNA detected in the same participants' ONP swabs and with no correlation among EB and ONP. Nevertheless, since the results may vary based on the methodology applied, in the following assessment, it is conservatively assumed that the initial viral load λ<sup>0</sup> is equal to the one present in ONP swab.

Defined *Vj* as the average volume of a droplet emitted in the *j*th dimensional interval [mL], the released virions are calculated as in Eq. (5), while in Eq. (6), the worst case is defined

$$N\_{\text{virtions},\mu} = \sum\_{j=1}^{M} N\_{\text{droplet},j,\mu} \times \left( V\_j || \times \lambda\_0 \right) \tag{5}$$

$$N\_{\text{virions},99\%} = \sum\_{j=1}^{M} N\_{\text{droplet},j,99\%} \times \left(V\_j || \times \lambda\_{\text{viral}}\right). \tag{6}$$

To calculate the emission rate in the case of speech, the values are multiplied by 0.6 to have [virions/min]. In the cough case, the values are divided by 20 to have an emission rate in [virions/cough].
