The COVID-19 pandemic necessitates a thorough understanding of infection transmission mechanisms, particularly aerosol transmission, to safely resume economic activities. While contact and droplet transmission are considered primary routes, airborne transmission has gained prominence following reports of superspreading events. The World Health Organization (WHO) and Centers for Disease Control and Prevention (CDC) acknowledge the possibility of airborne transmission under specific conditions, such as poorly ventilated enclosed spaces and prolonged exposure to severely infected individuals. However, critical data, such as the minimum infectious dose for SARS-CoV-2, the relationship between disease severity and viral load, and the proportion of airborne infections, are still lacking. This knowledge gap is especially significant when considering transmission from asymptomatic or mildly symptomatic individuals, where even mask leaks can facilitate airborne spread. Recent outbreaks in air-conditioned restaurants highlight the potential for virus-laden aerosols to travel significant distances and cause infection. The size distribution of airborne contaminants is crucial for evaluating their risk potential, inhalability, deposition sites in the respiratory tract, air transport, and removal by control technologies. Expiratory activities generate aerosols ranging from 0.05 to 500 µm, with submicron droplets and droplet nuclei (formed by evaporation) containing viruses (0.02-0.3 µm). These droplets, containing soluble non-volatile materials, typically decrease in diameter by half during evaporation. Droplets under 20 µm (10 µm desiccated residue), key in airborne transmission, dry up within seconds, forming non-volatile residues containing viral particles.

The literature on airborne transmission risk has grown substantially over the past decade. Studies on influenza have indicated a significant proportion (42-63%) of virus-containing droplets are in the respirable size range, supporting airborne transmission. This has crucial implications for post-lockdown economic activity. The perception of airborne risk, especially in enclosed spaces, even with mask use, can significantly impact business and office interactions. Therefore, effective mitigation and sanitization technologies are needed to build confidence and facilitate economic recovery. Existing research on airborne risk, as reviewed by Tellier et al., has explored the influence of droplet size on risk, inhalability, deposition, transport, and removal. Previous studies on the size distributions of respiratory droplets, which vary based on the type of expiratory activity (breathing, speaking, coughing, sneezing), have highlighted the complexity of this phenomenon. Viral loading in these droplets varies widely (10² to 10¹¹ copies/mL) and its distribution across different size droplets is not consistently understood. While some studies support the use of a Poisson distribution to model viral incorporation, others have questioned this assumption. Stadnytskyi et al. estimated the percentage of droplets (prior to dehydration) containing at least one virus based on viral load, highlighting the role of Poisson fluctuations in generating droplets without any virus.

The study uses the theory of atomization of suspensions and radioactive aerosol activation mechanisms to model the distribution of viruses in droplets. The average virus concentration (Cv) in respiratory fluids (RNA copies/mL) is used to calculate the mean expected number (μ) of viral copies in a droplet of diameter (dp): μ = (π/6)dp³Cv. μ is considered the propensity parameter for virus-laden particle (virusol) formation. The probability (Pn) that a droplet contains n viral copies follows a Poisson distribution: Pn = (μn/n!)exp(-μ). The probability of a droplet containing no virus (n=0) is e-μ. The complementary probability (Pv) that a droplet contains at least one virus (and is therefore a virusol) is Pv = 1 – e-μ. The authors utilize data on viral load from various studies (Table 1), categorized into mild-to-moderate cases (10²/mL < Cv < 2 × 10⁵/mL) and severe cases (Cv ≥ 2 × 10⁵/mL). Data on droplet size distributions from previous studies (Tables 2 and 3) are employed, primarily focusing on droplets less than 20 µm in diameter (equivalent to 10 µm after desiccation). Equation (3) provides the fraction of virus-laden droplets and is graphically represented in Figure 1. Figure 2 illustrates the relationship between viral load and the cut-off diameter below which the virus-laden fraction falls below 0.01%, 0.1%, and 1%. For polydisperse droplets, a lognormal distribution is assumed. Equation (4) calculates the fraction (Fv) of virus-laden droplets in a lognormal distribution, considering the median propensity parameter (μG). Figure 3 shows the variation of the virusol fraction with the median propensity parameter for different geometric standard deviations (GSDs). Figure 4 presents the normalized virusol size distributions compared to original droplet distributions for various propensity parameters. Finally, Figure 5 shows the ratio of virusol and original droplet volume median diameters (VMDs) as a function of the median propensity parameter for different GSDs.

The study reveals that for mild-to-moderate COVID-19 cases, with viral loads typically below 2 × 10⁵ RNA copies/mL, the fraction of virus-laden droplets under 20 µm (before evaporation, corresponding to 10 µm after evaporation) is extremely low. This suggests that aerosol transmission from these cases is unlikely. Figure 1 graphically illustrates this point, showing that the fraction of virus-laden droplets is significantly less than 0.1% for droplets smaller than 60 µm in these low-viral-load cases. Figure 2 further confirms this by showing the cut-off diameters for different virus-laden fractions as a function of viral load. Considering the low number of droplets likely to leak from masks and stay airborne (<1000), a virus-laden fraction of 0.1% or less is deemed sufficiently safe, implying less than one virus-carrying droplet per ejection event. Even in severe cases with high viral loads, droplets smaller than 2 µm (before evaporation) are unlikely to be contaminated. Analysis of droplet size distributions (Tables 2 and 3) and virus-laden fractions shows that the risk of inhaling even one virus-carrying droplet is extremely low in real-world scenarios, indicating that only large droplets pose a significant risk. The study also investigates the impact of Poisson fluctuations on the size distribution of virus-laden droplets (virusols) in polydisperse systems. For lognormally distributed droplets, the study develops a model (Equation 4) to predict the virusol fraction. Figures 3 and 5 demonstrate a shift in the virusol size distribution towards larger particles compared to the original droplet distribution, with the median size of virusols being 1.5 to 20 times higher than that of the original droplets. The geometric standard deviation of the virusol distribution is generally smaller than that of the original droplet distribution due to a “statistical barrier” against viral incorporation into smaller droplets.

The findings highlight the importance of considering Poisson fluctuations in modeling the distribution of viruses in respiratory droplets. The results suggest that aerosol transmission of COVID-19 is more likely to occur from individuals with severe infections and larger droplets, rather than from those with mild to moderate cases. This has significant implications for infection control strategies. The significant upward shift in virusol size implies shorter residence times in indoor environments, which is relevant to risk assessment and the design of ventilation systems. The study also provides a method to convert original droplet size distributions to virus-laden droplet size distributions, offering a more accurate representation of the aerosols responsible for infection transmission. The relatively low probability of virus contamination in small droplets suggests that coarser filters, with lower flow resistance and higher clean air delivery rates, could be sufficient for mitigating airborne infection risks.

This study underscores the role of Poisson fluctuations in determining the size distribution of virus-laden droplets and its implications for airborne transmission of COVID-19. The analysis demonstrates that aerosol transmission is more likely from individuals with severe infections. For mild-to-moderate cases, the risk of infection via airborne droplets below 20µm is negligible. This finding could influence the design and efficiency of air filtration systems, suggesting that coarser filters might suffice, reducing flow resistance and enhancing clean air delivery rates. Future research could focus on obtaining more comprehensive data on droplet size distributions under various conditions and exploring the interplay of different factors influencing viral transmission.

The study relies on existing data from previous studies on droplet size distributions and viral loads, which might not fully capture the diversity of real-world scenarios. The assumptions of lognormal distribution and the Poisson model could introduce some uncertainties. Further research involving more comprehensive datasets and more detailed experimental measurements is needed to validate the findings and improve model accuracy. The available data on viral loads and droplet size distributions is limited and shows significant variability.