# Triggering of an Epidemic Outbreak via Long-Range Atmospheric Transport of Bio-Aerosols—Application to a Hypothetical Case for COVID-19

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Long-Distance Transport of Both Inert and Bio-Aerosols

_{2.5}) from biomass burnings [26], and pollen transport from eastern North America to Greenland ([27] and references therein). These phenomena are well studied and documented, and their importance has been evaluated. Except for pollen, these examples refer to non-biological, inert matter and are cited from the point of view of the coupling of observation and simulation to understand the modes and parameters associated with their transmission and to demonstrate that long-distance travel can give rise to physical effects from these particles. Aerosols containing biological matter either made of living or non-living components are usually named bio-aerosols.

_{50}values (50% tissue culture infective dose) allowing the risk of infection to be assessed.

## 3. Outdoor Airborne Transmission of Pathogens: Extension of a Wells–Riley Type Model

#### 3.1. Basic Concepts in (Indoor and Outdoor) Airborne Transmission

^{−3}units), ${n}_{q}\left(\overrightarrow{r,}t\right)$, the inhaled dose X during a time of exposure t, can be written as:

^{3}/h in the present investigation). Note that this definition of the dose does not require a homogeneous distribution of quanta in space. Only ${n}_{q}\left(\overrightarrow{r,}t\right)$ at the inhaled location (mouth and nostrils) has to be considered. Note also that due to the extremely low concentration of quanta in air, ${n}_{q}\left(\overrightarrow{r,}t\right)$ is not really a continuous function of $\overrightarrow{r,}t$ (since a number of viruses is of course an integer) but can be treated as such due to the stochastic character of the problem and the search for a statistical solution. When the quantum concentration can be considered as being constant during the time of exposure, then the dose X expression simplifies to:

#### 3.2. Box Model of Outdoor Transmission

#### 3.3. Possible Airborne Epidemic Triggering via Long-Range Transmission

_{1}, it is possible to quantify the quantum concentration n

_{1},

_{q}(L

_{1}) following Equation (8) taking into account that at the upstream border of the source n

_{1,q}(x

_{1}= 0) = 0. The downwind border of the source also coincides with the upwind border of the “no man’s land” section (hereafter box 2). However, as explained further in Section 4.2, the dispersive height H in box 2 (H

_{2}) is higher than in box 1 (H

_{1}). This impacts the initial quantum concentration n

_{2,q}(x

_{2}= 0) by a factor of H

_{1}/H

_{2}at the upstream border of box 2 such that:

_{2,q}(x

_{2}= 0) = H

_{1}/H

_{2}× n

_{1,q}(L

_{1})

_{2,q}(x

_{2}) in box 2 is then governed only by the virus lifetime according to Equation (9) since ${D}_{I}=0$ in box 2. This leads to a new value n

_{2},

_{q}(L

_{2}) at the downstream border L

_{2}of box 2. Again, this border coincides with the upstream border of the target area, box 3. At this interface, however, the dispersive height is not modified compared to box 2 (H

_{3}= H

_{2}) since H

_{2}is already taken as an upper limit of the ABL thickness (see Section 4.2). The quantum concentration entering box 3 is then n

_{3,q}(x

_{3}= 0) = n

_{2,q}(L

_{2}). The quantum concentration n

_{3,q}(x

_{3}) can be considered as spatially and temporally constant within box 3 provided that:

- The pathogen lifetime is clearly larger than the hydrodynamic time within the target depth, which is typically around 10–20 km.
- The width of the target is less than the width of the source.
- The emission source rate and meteorology do not change significantly during the time of exposure.

## 4. Results for a Hypothetical Case of Long-Range Transmission of COVID-19 from Southern England to Northern France

#### 4.1. General Considerations

#### 4.2. Details of the Long-Range Model of Transmission for the Present Hypothetical Case

_{1}of 45 km, an area inside which we assume a population N

_{p}(x

_{1}= 45 km) of 11 million people.

_{1},

_{q}(L

_{1}) at the downwind border of this source box. However, the following problem arises: in wintertime, most of the quanta will be emitted indoors, with a room temperature around 20 °C and a rather low relative humidity (RH) (we assume 35% as a mean), but outdoors they are transported by the wind at low temperature (around 5 °C) and rather high humidity (80%) conditions, where the virus lifetime (see discussion in Section 5) is expected to be much longer than the atmospheric transport (hydrodynamic) time. Therefore, viral inactivation, as discussed in Section 5.2, will only occur indoors, via thermal effects at rather low RH. Indoor air is continuously renewed as contaminated air is evacuated outdoors with a characteristic time equal to $1/ACH$ where $ACH$ is the number of times that the total air volume in a room is completely removed and replaced in an hour. Therefore, the effect of viral inactivation indoors prior to evacuation can be taken as a reduction of the quantum emission rate per infector used in Section 3.2 following the formula:

_{1}= 45 km and state D in Figure 2), the population within the source is assumed as $1.1\times {10}^{7}$, the wind velocity taken as 30 km/h, the width of the source as W = 40 km (which influences the density of infectors if Equation (10) is used in place of (12)), and the quantum production rate of an infector as 10 h

^{−1}. The numerical application leads to ${n}_{1,q}\left(45\mathrm{km}\right)=7.15\times {10}^{-6}{\mathrm{m}}^{-3}$ assuming a proportion of infected persons of r = 0.03 in the greater London area.

_{2},

_{q}(L

_{2}) = n

_{2},

_{q}(x

_{2}= 0). Using a conservative estimate for $H$of 1000 m, a value corresponding to a common upper value of ABL thickness for neutral or stable conditions [46] results in a numerical value of ${n}_{3,q}\left({x}_{3}=0\right)$ of $2.15\times {10}^{-6}{\mathrm{m}}^{-3}$ at the upstream border of one of our targets.

^{6}and 1.2 × 10

^{6}people, respectively. We assume that the wind direction is the same as the direct path between the source and the target, a dominant direction in wintertime, which roughly corresponds to a wind direction from the west/northwest (respectively 288 and 294 degrees). As before, we also assume a wind velocity of 30 km/h, which is only slightly higher than the mean wind velocity in February/early March [55]. Note again that both target areas have a width across the wind less than that of the source. Table 1 gathers the main characteristics of the three boxes as depicted in Figure 3. Table 2 summarizes the assumed values of various parameters leading to a statistical number of primary cases. Since this number appears to be a few units in the frame of our assumptions, it clearly reveals the potential for an infection being triggered through long-range transportation of airborne viruses.

## 5. Discussion

#### 5.1. Validity of the Atmospheric Box Model

^{−14}m

^{−3}over northeastern France. Using the effective quantum production rate q

_{eff}value derived from Table 2, the unit emission HYSPLIT values (through the expression: N

_{P}× r × q

_{eff}× 24) yield a quantum concentration of 3.1 × 10

^{−6}quantum m

^{−3}, which is very close to the upstream box model value of 2.1 × 10

^{−6}. Due to the line source configuration, lateral dispersion along the centerline would be negligible, and the concentration results would primarily depend upon the vertical mixing. An examination of the diagnostic vertical mass profile after 12 h (not shown) indicates that 94% of the mass was in the first 1200 m above ground and 99% was within the first 1500 m, consistent with the well-mixed box model assumptions.

#### 5.2. The Question of the Virus Lifetime Indoor and Outdoor in Bio-Aerosol Form

^{−1}), and it is generally admitted [61,63] that, for a given value of RH, it follows an Arrhenius law with temperature:

^{21}min

^{−1}, respectively.

#### 5.3. The Very Low Dose Question

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Giesecke, J. Primary and index cases. Lancet
**2014**, 384, 2024. [Google Scholar] [CrossRef] [PubMed] - MaGee, J.; Arora, V.; Ventresca, M. Identifying the source of an epidemic using particle swarm optimization. In Proceedings of the 2022 Genetic and Evolutionary Computation Conference (Gecco’22), Boston, MA, USA, 9–13 July 2022; pp. 1237–1244. [Google Scholar]
- Snow, J. On the Mode of Communication of Cholera, 2nd ed.; John Churchill: London, UK, 1855. [Google Scholar]
- Carinci, F. COVID-19: Preparedness, decentralisation, and the hunt for patient zero Lessons from the Italian outbreak. Br. Med. J.
**2020**, 368, 1–2. [Google Scholar] - Lu, D. The hunt to find the coronavirus pandemic’s patient zero. New Sci.
**2020**, 245, 9. [Google Scholar] [CrossRef] [PubMed] - Rowe, B.R.; Canosa, A.; Meslem, A.; Rowe, F. Increased airborne transmission of COVID-19 with new variants, Implications for health policies. Build. Environ.
**2022**, 219, 109132. [Google Scholar] [CrossRef] [PubMed] - Tang, J.W.; Bahnfleth, W.P.; Bluyssen, P.M.; Buonanno, G.; Jimenez, J.L.; Kurnitski, J.; Li, Y.; Miller, S.; Sekhar, C.; Morawska, L.; et al. Dismantling myths on the airborne transmission of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2). J. Hosp. Infect.
**2021**, 110, 89–96. [Google Scholar] [CrossRef] - Greenhalgh, T.; Jimenez, J.L.; Prather, K.A.; Tufekci, Z.; Fisman, D.; Schooley, R. Ten scientific reasons in support of airborne transmission of SARS-CoV-2. Lancet
**2021**, 397, 1603–1605. [Google Scholar] [CrossRef] - Morawska, L.; Tang, J.L.W.; Bahnfleth, W.; Bluyssen, P.M.; Boerstra, A.; Buonanno, G.; Cao, J.J.; Dancer, S.; Floto, A.; Franchimon, F.; et al. How can airborne transmission of COVID-19 indoors be minimised? Environ. Int.
**2020**, 142, 105832. [Google Scholar] [CrossRef] - Randall, K.; Ewing, E.; Marr, L.; Jimenez, J.L.; Bourouiba, L. How did we get here: What are droplets and aerosols and how far do they go? A historical perspective on the transmission of respiratory infectious diseases. Interf. Foc.
**2021**, 11, 20210049. [Google Scholar] [CrossRef] - Wang, C.C.; Prather, K.A.; Sznitman, J.; Jimenez, J.L.; Lakdawala, S.S.; Tufekci, Z.; Marr, L.C. Airborne transmission of respiratory viruses. Science
**2021**, 373, eabd9149. [Google Scholar] [CrossRef] - Morawska, L.; Cao, J. Airborne Transmission of SARS-CoV-2: The World Should Face the Reality. Environ. Int.
**2020**, 139, 105730. [Google Scholar] [CrossRef] - New York Times 239 Experts with One Big Claim the Coronavirus is Airborne. 2021. Available online: https://www.nytimes.com/2020/07/04/health/239-experts-with-one-big-claim-the-coronavirus-is-airborne.html (accessed on 1 June 2021).
- Rowe, B.R.; Canosa, A.; Drouffe, J.M.; Mitchell, J.B.A. Simple quantitative assessment of the outdoor versus indoor airborne transmission of viruses and COVID-19. Environ. Res.
**2021**, 198, 111189. [Google Scholar] [CrossRef] - Wells, W.F. Airborne Contagion and Air Hygiene. An Ecological Study of Droplet Infections; Harvard University Press: Cambridge, MA, USA, 1955. [Google Scholar]
- Riley, E.C.; Murphy, G.; Riley, R.L. Airborne Spread of Measles in A Suburban Elementary-School. Am. J. Epidemiol.
**1978**, 107, 421–432. [Google Scholar] [CrossRef] - Ortolano, L. Estimating Air Quality Impacts. Environ. Impact. Assess. Rev.
**1985**, 5, 9–35. [Google Scholar] [CrossRef] - Khan, S.; Hassan, Q. Review of developments in air quality modelling and air quality dispersion models. J. Environ. Eng. Sci.
**2021**, 16, 1–10. [Google Scholar] [CrossRef] - Brouwer, A.F.; Weir, M.H.; Eisenberg, M.C.; Meza, R.; Eisenberg, J.N.S. Dose-response relationships for environmentally mediated infectious disease transmission models. PLoS Comput. Biol.
**2017**, 13, e1005481. [Google Scholar] [CrossRef] [Green Version] - Haas, C.N.; Rose, J.B.; Gerba, C.P. Quantitative Microbial Risk Assessment; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2014. [Google Scholar]
- Teunis, P.F.M.; Havelaar, A.H. The Beta Poisson dose-response model is not a single-hit model. Risk Anal.
**2000**, 20, 513–520. [Google Scholar] [CrossRef] [PubMed] - Zwart, M.P.; Hemerik, L.; Cory, J.S.; de Visser, J.; Bianchi, F.J.; Van Oers, M.M.; Vlak, J.M.; Hoekstra, R.F.; Van der Werf, W. An experimental test of the independent action hypothesis in virus-insect pathosystems. Proc. R. Soc. B Biol. Sci.
**2009**, 276, 2233–2242. [Google Scholar] [CrossRef] [Green Version] - Fuchs, N.A. The Mechanics of Aerosols; Dover Publication: Mineola, NY, USA, 1989. [Google Scholar]
- Francis, D.; Fonseca, R.; Nelli, N.; Bozkurt, D.; Picard, G.; Guan, B. Atmospheric rivers drive exceptional Saharan dust transport towards Europe. Atmos. Res.
**2022**, 266, 105959. [Google Scholar] [CrossRef] - Allen, S.; Allen, D.; Baladima, F.; Phoenix, V.R.; Thomas, J.L.; Le Roux, G.; Sonke, J.E. Evidence of free tropospheric and long-range transport of microplastic at Pic du Midi Observatory. Nat. Com.
**2021**, 12, 7242. [Google Scholar] [CrossRef] - Martins, L.D.; Hallak, R.; Alves, R.C.; de Almeida, D.S.; Squizzato, R.; Moreira, C.A.B.; Beal, A.; da Silva, I.; Rudke, A.; Martins, J.A. Long-range Transport of Aerosols from Biomass Burning over Southeastern South America and their Implications on Air Quality. Aerosol Air Qual. Res.
**2018**, 18, 1734–1745. [Google Scholar] [CrossRef] [Green Version] - Rousseau, D.D.; Duzer, D.; Cambon, G.V.; Jolly, D.; Poulsen, U.; Ferrier, J.; Schevin, P.; Gros, R. Long distance transport of pollen to Greenland. Geophys. Res. Lett.
**2003**, 30, 1765. [Google Scholar] [CrossRef] - Dillon, C.F.; Dillon, M.B. Multiscale Airborne Infectious Disease Transmission. Appl. Environ. Microbiol.
**2021**, 87, e02314-20. [Google Scholar] [CrossRef] [PubMed] - Donaldson, A.I.; Gloster, J.; Harvey, L.D.J.; Deans, D.H. Use of prediction models to forecast and analyse airborne spread during the foot-and-mouth disease outbreaks in Brittany, Jersey and the Isle of Wight in 1981. Veter. Rec.
**1982**, 110, 53–57. [Google Scholar] [CrossRef] - Garner, M.; Hess, G.; Yang, X. An integrated modelling approach to assess the risk of wind-borne spread of foot-and-mouth disease virus from infected premises. Environ. Mod. Assess.
**2006**, 11, 195–207. [Google Scholar] [CrossRef] - Gloster, J.; Sellers, R.F.; Donaldson, A.I. Long distance transport of foot-and-mouth disease virus over the sea. Veter. Rec.
**1982**, 110, 47–52. [Google Scholar] [CrossRef] - Hagerman, A.D.; South, D.D.; Sondgerath, T.C.; Patyk, K.A.; Sanson, R.L.; Schumacher, R.S.; Delgado, A.H.; Magzamen, S. Temporal and geographic distribution of weather conditions favorable to airborne spread of foot-and-mouth disease in the coterminous United States. Prev. Veter. Med.
**2018**, 161, 41–49. [Google Scholar] [CrossRef] - La, A.; Zhang, Q.; Cicek, N.; Coombs, K.M. Current understanding of the airborne transmission of important viral animal pathogens in spreading disease. Biosyst. Eng.
**2022**, 224, 92–117. [Google Scholar] [CrossRef] - Lambkin, K.; Hamilton, J.; McGrath, G.; Dando, P.; Draxler, R. Foot and Mouth Disease atmospheric dispersion system. Adv. Sci. Res.
**2019**, 16, 113–117. [Google Scholar] [CrossRef] [Green Version] - Gloster, J.; Jones, A.; Redington, A.; Burgin, L.; Sorensen, J.H.; Turner, R.; Dillon, M.; Hullinger, P.; Simpson, M.; Astrup, P.; et al. Airborne spread of foot-and-mouth disease-Model intercomparison. Veter. J.
**2010**, 183, 278–286. [Google Scholar] [CrossRef] [Green Version] - Coffman, M.S.; Sanderson, M.; Dodd, C.C.; Arzt, J.; Renter, D.G. Estimation of foot-and-mouth disease windborne transmission risk from USA beef feedlots. Prev. Veter. Med.
**2021**, 195, 105453. [Google Scholar] [CrossRef] [PubMed] - Zhao, Y.; Richardson, B.; Takle, E.; Chai, L.L.; Schmitt, D.; Xin, H.W. Airborne transmission may have played a role in the spread of 2015 highly pathogenic avian influenza outbreaks in the United States. Sci. Rep.
**2019**, 9, 11755. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cannon, R.M.; Garner, M.G. Assessing the risk of wind-borne spread of foot-and-mouth disease in Australia. Environ. Int.
**1999**, 25, 713–723. [Google Scholar] [CrossRef] - Sutmoller, P.; Vose, D.J. Contamination of animal products: The minimum pathogen dose required to initiate infection. Rev. Sci. Tech. Off. Int. Epizoot.
**1997**, 16, 30–32. [Google Scholar] [CrossRef] - Mareddy, A.R. Impacts on air environment. In Environmental Impact Assessment: Theory and Practice; Elsevier, Inc.: Amsterdam, The Netherlands, 2017; pp. 171–216. [Google Scholar]
- Canter, L.W. Air Quality Impacts. In Environmental Impacts of Agricultural Production Activities; CRC Press: Boca Raton, FL, USA, 1986; pp. 169–224. [Google Scholar]
- Nelson, K.E.; LaBelle, S.J. Handbook for the Review of Airport Environmental Impact Statements; ANL/ES-46; Argonne National Laboratory: Argonne, IL, USA, 1975. [Google Scholar]
- Gifford, F.A. Use of Routine Meteorological Observations for Estimating Atmospheric Dispersion. Nucl. Saf.
**1961**, 2, 47–51. [Google Scholar] - Pasquill, F. The estimation of the dispersion of windborn material. Meteorol. Mag.
**1961**, 90, 33–49. [Google Scholar] - Turner, D.B. Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed.; CRC Press, Lewis Publishers: Boca Raton, FL, USA, 1994. [Google Scholar]
- Sáez de Cámara Oleaga, E. Air Pollution and Its Control Technologies. 2016. Available online: https://ocw.ehu.eus/course/view.php?id=389 (accessed on 12 January 2022).
- Seinfeld, J.H.; Pandis, S.N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 3rd ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2016. [Google Scholar]
- Turner, D.B. Workbook of Atmospheric Dispersion Estimates; U.S. Environmental Protection Agency, Office of Air Programs: Chapel Hill, NC, USA, 1970; Volume AP-26. [Google Scholar]
- Hsu, S.A.; Meindl, E.A.; Gilhousen, D.B. Determining the Power-Law Wind-Profile Exponent Under Near-Neutral Stability Conditions at Sea. J. Appl. Meteorol.
**1994**, 33, 757–765. [Google Scholar] [CrossRef] - Nicas, M.; Nazaroff, W.W.; Hubbard, A. Toward understanding the risk of secondary airborne infection: Emission of respirable pathogens. J. Occup. Environ. Hyg.
**2005**, 2, 143–154. [Google Scholar] [CrossRef] - van Doremalen, N.; Bushmaker, T.; Morris, D.H.; Holbrook, M.G.; Gamble, A.; Williamson, B.N.; Tamin, A.; Harcourt, J.L.; Thornburg, N.J.; Gerber, S.I.; et al. Aerosol and Surface Stability of SARS-CoV-2 as Compared with SARS-CoV-1. N. Eng. J. Med.
**2020**, 382, 1564–1567. [Google Scholar] [CrossRef] - Lytle, C.D.; Sagripanti, J.L. Predicted inactivation of viruses of relevance to biodefense by solar radiation. J. Virol.
**2005**, 79, 14244–14252. [Google Scholar] [CrossRef] [Green Version] - Sagripanti, J.L.; Lytle, C. Estimated Inactivation of Coronaviruses by Solar Radiation With Special Reference to COVID-19. Photochem. Photobiol.
**2020**, 96, 731–737. [Google Scholar] [CrossRef] - Weather and Climate Average Humidity in London. 2022. Available online: https://weather-and-climate.com/average-monthly-Humidity-perc,London,United-Kingdom (accessed on 1 March 2022).
- Weather Sparks Weather in London. 2022. Available online: https://weatherspark.com/d/45062/2/11/Average-Weather-on-February-11-in-London-United-Kingdom#Figures-WindDirection (accessed on 1 March 2022).
- Stein, A.F.; Draxler, R.R.; Rolph, G.D.; Stunder, B.J.B.; Cohen, M.D.; Ngan, F. NOAA’s HYSPLIT Atmospheric Transport and Dispersion Modeling System. Bull. Am. Meteor. Soc.
**2015**, 96, 2059–2077. [Google Scholar] [CrossRef] - National Centers for Environmental Information Global Data Assimilation System (GDAS). 2022. Available online: https://www.ncei.noaa.gov/access/metadata/landing-page/bin/iso?id=gov.noaa.ncdc:C00379 (accessed on 3 March 2022).
- Ijaz, M.K.; Brunner, A.H.; Sattar, S.A.; Nair, R.C.; Johnsonlussenburg, C.M. Survival Characteristics of Airborne Human Coronavirus-229E. J. Gen. Virol.
**1985**, 66, 2743–2748. [Google Scholar] [CrossRef] [PubMed] - Yang, W.; Marr, L.C. Mechanisms by Which Ambient Humidity May Affect Viruses in Aerosols. Appl. Envir. Microbiol.
**2012**, 78, 6781–6788. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Marr, L.C.; Tang, J.W.; Van Mullekom, J.; Lakdawala, S.S. Mechanistic insights into the effect of humidity on airborne influenza virus survival, transmission and incidence. J. R. Soc. Interf.
**2019**, 16, 20180298. [Google Scholar] [CrossRef] - Morris, D.H.; Yinda, K.C.; Gamble, A.; Rossine, F.W.; Huang, Q.S.; Bushmaker, T.; Fischer, R.J.; Matson, M.J.; Van Doremalen, N.; Vikesland, P.J.; et al. Mechanistic theory predicts the effects of temperature and humidity on inactivation of SARS-CoV-2 and other enveloped viruses. eLife
**2021**, 10, e65902. [Google Scholar] [CrossRef] - Horst, D.; Zhang, Q.; Schmidt, E. Deliquescence and Efflorescence of Hygroscopic Salt Particles in Dust Cakes on Surface Filters. Chem. Eng. Technol.
**2019**, 42, 2348–2357. [Google Scholar] [CrossRef] - Yap, T.F.; Liu, Z.; Shveda, R.A.; Preston, D.J. A predictive model of the temperature-dependent inactivation of coronaviruses. Appl. Phys. Lett.
**2020**, 117, 060601. [Google Scholar] [CrossRef] - Fears, A.C.; Klimstra, W.B.; Duprex, P.; Hartman, A.; Weaver, S.C.; Plante, K.S.; Mirchandani, D.; Plante, J.A.; Aguilar, P.V.; Fernandez, D.; et al. Persistence of Severe Acute Respiratory Syndrome Coronavirus 2 in Aerosol Suspensions. Emerg. Infect. Dis.
**2020**, 26, 2168–2171. [Google Scholar] [CrossRef] - Oswin, H.P.; Haddrell, A.E.; Otero-Fernandez, M.; Mann, J.F.S.; Cogan, T.A.; Hilditch, T.G.; Tiana, J.; Hardya, D.A.; Hill, D.J.; Finn, A.; et al. The dynamics of SARS-CoV-2 infectivity with changes in aerosol microenvironment. Proc. Natl. Acad. Sci. USA
**2022**, 119, e2200109119. [Google Scholar] [CrossRef] - Smither, S.J.; Eastaugh, L.S.; Findlay, J.S.; Lever, M.S. Experimental aerosol survival of SARS-CoV-2 in artificial saliva and tissue culture media at medium and high humidity. Emerg. Microb. Infect.
**2020**, 9, 1415–1417. [Google Scholar] [CrossRef] - Druett, H.A.; May, K.R. Unstable Germicidal Pollutant in Rural Air. Nature
**1968**, 220, 395–396. [Google Scholar] [CrossRef] - May, K.R.; Druett, H.A. A Microthread Technique for Studying Viability of Microbes in a Simulated Airborne State. J. Gen. Microbiol.
**1968**, 51, 353–366. [Google Scholar] [CrossRef] [Green Version] - Donaldson, A.I.; Ferris, N.P. The Survival of Foot-and-Mouth-Disease Virus in Open Air Conditions. J. Hyg.
**1975**, 74, 409–416. [Google Scholar] [CrossRef] [Green Version] - Hood, A. The effect of open-air factors on the virulence and viability of airborne Francisella tularensis. Epidemiol. Infect.
**2009**, 137, 753–761. [Google Scholar] [CrossRef] [Green Version] - Cox, R.; Ammann, M.; Crowley, J.N.; Griffiths, P.T.; Herrmann, H.; Hoffmann, E.H.; Jenkin, M.E.; McNeill, V.; Mellouki, A.; Penkett, C.J.; et al. Opinion: The germicidal effect of ambient air (open-air factor) revisited. Atmos. Chem. Phys.
**2021**, 21, 13011–13018. [Google Scholar] [CrossRef] - Hobday, R.; Collignon, P. An Old Defence Against New Infections: The Open-Air Factor and COVID-19. Cureus J. Med. Sci.
**2022**, 14, e26133. [Google Scholar] [CrossRef] [PubMed] - Hobday, R. The open-air factor and infection control. J. Hosp. Infect.
**2019**, 103, E23–E24. [Google Scholar] [CrossRef] [PubMed] - Buonanno, G.; Morawska, L.; Stabile, L. Quantitative assessment of the risk of airborne transmission of SARS-CoV-2 infection: Prospective and retrospective applications. Environ. Int.
**2020**, 145, 106112. [Google Scholar] [CrossRef] [PubMed] - Levetin, E. Aerobiology of Agricultural Pathogens. In Manual of Environmental Microbiology; Yates, M.V., Nakatsu, C.H., Miller, R.V., Pillai, S.D., Eds.; Wiley Online Library: Hoboken, NJ, USA, 2015; pp. 1–20. [Google Scholar]
- France Info COVID-19: Le Variant Anglais Détecté dans 68% des Tests Positifs à Dunkerque. 2021. Available online: https://www.francetvinfo.fr/sante/maladie/coronavirus/COVID-19-le-variant-anglais-detecte-dans-68-des-tests-positifs-a-dunkerque_4293213.html (accessed on 15 February 2021).

**Figure 2.**Vertical dispersion length for Gaussian plumes. Classification of atmosphere state: A: Extremely unstable; B: Moderately unstable; C: slightly unstable; D: neutral; E: slightly stable; F: moderately stable.

**Figure 3.**Model of three boxes between greater London and northern France. Note that the upstream border of box 3 is dependent on the considered target (i.e., either Dunkerque or Lille).

Box 1 | Box 2 | Box 3 | |
---|---|---|---|

Length: L (km) | 45 | 150/230 ^{a} | --- ^{b} |

Width: W (km) | 40 | 40 | <40 |

Dispersive height: H (m) | 300 | 1000 | 1000 |

Wind speed V_{∞} (km/h) | 30 | 30 | 30 |

n_{q} (quanta/m^{3}) | 7.1 × 10^{−6 c} | 2.1 × 10^{−6} | 2.1 × 10^{−6} |

^{a}: Depending on the considered target, either Dunkerque or Lille.

^{b}: This length is not fixed since it is not useful for the present estimation.

^{c}: Value at the downstream end of the box.

**Table 2.**Possible number of primary cases created (per day) via the long-distance transport of aerosols. London area population of 11 million; wind velocity: 30 km/h; exposure of 24 h; proportion of possible infectors in greater London: r = 3%; quantum production rate q = 10 h

^{−1}/infector.

Dunkerque | Lille | |
---|---|---|

Distance from London, center to center (km) | 180 | 244 |

Population (10^{6}) | 0.2 | 1.2 |

Hydrodynamic time (h) | 5.0 | 7.7 |

Upstream quantum concentration (m^{−3}) | 2.1 × 10^{−6} | 2.1 × 10^{−6} |

Dose for 24 h | 2.6 × 10^{−5} | 2.6 × 10^{−5} |

Probability of infection P_{t} | 2.6 × 10^{−5} | 2.6 × 10^{−5} |

Number of primary cases | 5 | 31 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rowe, B.R.; Mitchell, J.B.A.; Canosa, A.; Draxler, R.
Triggering of an Epidemic Outbreak via Long-Range Atmospheric Transport of Bio-Aerosols—Application to a Hypothetical Case for COVID-19. *Atmosphere* **2023**, *14*, 1050.
https://doi.org/10.3390/atmos14061050

**AMA Style**

Rowe BR, Mitchell JBA, Canosa A, Draxler R.
Triggering of an Epidemic Outbreak via Long-Range Atmospheric Transport of Bio-Aerosols—Application to a Hypothetical Case for COVID-19. *Atmosphere*. 2023; 14(6):1050.
https://doi.org/10.3390/atmos14061050

**Chicago/Turabian Style**

Rowe, Bertrand R., J. Brian A. Mitchell, André Canosa, and Roland Draxler.
2023. "Triggering of an Epidemic Outbreak via Long-Range Atmospheric Transport of Bio-Aerosols—Application to a Hypothetical Case for COVID-19" *Atmosphere* 14, no. 6: 1050.
https://doi.org/10.3390/atmos14061050