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(severe aerosol-borne 2 10 virus of order new the The on dose esti- infectious indoor we an distributions, mate best-characterized size drop respiratory the By with aerosols. from events of spreading respiratory data use the available mask the of of face synthesizing infectiousness dimensions and and filtration, activity occupants, air its respiratory time and rate, depends ventilation breathing their bound this of room, and how rates occupants demonstrate the of We on space. number enclosed the an exposure of in guideline “cumulative product dis- the safety on the airborne indoor bound of time,” an upper an models derive impose on to would order that build here in have We transmission proposed assessment it. ease been against risk has protect guideline for safety to is no tools COVID-19 developed, While been of indoor recently recognized. transmission an airborne widely through of now mixed importance continuously The droplets be space. aerosol to pathogen-bearing small from sufficiently protection that guideline little a predicated Rule, being offers for Six-Foot (received is the 2021 specifically economy 3, distancing, American March social Seinfeld on the H. of John revival Member current Board Editorial The by accepted and TX, Station, 2020) College 9, University, September A&M review Texas Zhang, Renyi by Edited 02139 MA Cambridge, Technology, of Institute a Bazant Z. Martin of transmission airborne COVID-19 indoor limit to guideline A PNAS eateto hmclEgneig ascuet nttt fTcnlg,Cmrde A019 and 02139; MA Cambridge, Technology, of Institute Massachusetts Engineering, Chemical of Department h i-otRl sasca itnigrcmedto by recommendation distancing social a is Rule Six-Foot The VD1 sa netospemnata perdin appeared has and that 2019 December pneumonia in China, infectious Province, Hubei an Wuhan, is OVID-19 ∗ 01Vl 1 o 7e2018995118 17 No. 118 Vol. 2021 ehr ul pnteeitn hoeia framework theoretical existing the upon build here We | netosaerosol infectious | norsft guideline safety indoor a,b,1 n onW .Bush M. W. John and | ibretransmission airborne | SARS-CoV-2 b e aeas ofimdtepeec fifciu SARS-CoV-2 infectious Stud- of presence (30). the ducts confirmed air also via have linked ies were apartments high-rise Korean whose a building of in residents implicated between also outbreak was COVID-19 Ningbo, the transmission to in Airborne distance (28). journey with case 23 bus uncorrelated index when the 2-h were within locations a Similarly, seated them on (25). 61 their infected individual China, of of were infected passengers 53 all initially 68 some the of not 10, of presumably ft March 6 infected, on that State practice were choir Washington attendees Chorale in Valley place Skagit exam- took 2.5-h-long “superspreading For the so-called (29). at indoors for occur ple, especially invariably 22), micron-scale which COVID- 17–19, (25–28), of events” 7, spread small, 5, the in (4, role relatively 19 dominant a plays with droplets aerosol associated to transmission micron a of fractions from 21). varying considerable (11, radii millimeters a with span scales, to drops of known the liquid range are reduce events the respiratory However, substantially by transmission. thus expelled large-drop will such Rule of Six-Foot risk the Com- (20). to the drops to pliance millimeter-scale roughly largest, corresponds the ft of 6 range that maximum reveals visual- events high-speed such Indeed, of exhalation 19). ization vigorous transmis- (5, most sneezing pathogen the and from coughing of ejected events, drops vector large primary the is the sion that assumption the BY) distributed under is article access open This ulse pi 3 2021. 13, April Published doi:10.1073/pnas.2018995118/-/DCSupplemental at online information supporting contains article This Editorial 1 the by invited editor guest a is R.Z. Submission. Direct PNAS Board. a is article J.W.M.B. This and interest.y paper. competing y M.Z.B. the no wrote declare J.W.M.B. research; authors and The M.Z.B. designed and data; J.W.M.B. analyzed M.Z.B. and research; performed M.Z.B. contributions: Author * owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To enepoe 9 10). 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ENGINEERING virions in respiratory aerosols (31) suspended in air samples col- airborne COVID-19 transmission (17, 18). We use a similar lected at distances as large as 16 ft from infected patients in a mathematical framework here in order to derive a simple safety hospital room (3). Further evidence for the dominance of indoor guideline. airborne transmission has come from an analysis of 7,324 early We begin by describing the dynamics of airborne pathogen in cases outside the Hubei Province, in 320 cities across mainland a well-mixed room, on the basis of which we deduce an esti- China (32). The authors found that all clusters of three or more mate for the rate of inhalation of pathogen by its occupants. cases occurred indoors, 80% arising inside apartment homes and We proceed by deducing the associated infection rate from a 34% potentially involving public transportation; only a single single infected individual to a susceptible person. We illustrate transmission was recorded outdoors. Finally, the fact that face how the model’s epidemiological parameter, a measure of the mask directives have been more effective than either lockdowns infectiousness of COVID-19, may be estimated from available or social distancing in controlling the spread of COVID-19 (22, epidemiological data, including transmission rates in a number of 33) is consistent with indoor airborne transmission as the primary spreading events, and expiratory drop size distributions (11). Our driver of the global pandemic. estimates for this parameter are consistent with the pandemic The theoretical model developed herein informs the risk of status of COVID-19 in that they exceed those of SARS-CoV airborne transmission resulting from the inhalation of small, (17); however, our study calls for refined estimates through con- aerosol droplets that remain suspended for extended periods sideration of more such field data. Most importantly, our study within closed, well-mixed indoor spaces. When people cough, yields a safety guideline for mitigating airborne transmission via sneeze, sing, speak, or breathe, they expel an array of liquid limitation of indoor occupancy and exposure time, a guideline droplets formed by the shear-induced or capillary destabiliza- that allows for a simple quantitative assessment of risk in various tion of the mucosal linings of the lungs and respiratory tract settings. Finally, we consider the additional risk associated with (8, 34, 35) and saliva in the mouth (36, 37). When the person respiratory jets, which may be considerable when face masks are is infectious, these droplets of sputum are potentially pathogen not being worn. bearing, and represent the principle vector of disease transmis- sion. The range of the exhaled pathogens is determined by the The Well-Mixed Room radii of the carrier droplets, which typically lie in the range of We first characterize the evolution of the pathogen concentra- 0.1 µm to 1 mm. While the majority are submicron in scale, tion in a well-mixed room. The assumption of well mixedness the drop size distribution depends on the form of exhalation is widely applied in the theoretical modeling of indoor airborne event (11). For normal breathing, the drop radii vary between transmission (14, 16, 17), and its range of validity is discussed in 0.1 and 5.0 µm, with a peak around 0.5 µm (11, 38, 39). Rela- SI Appendix, section 1. We describe the evolution of the airborne tively large drops are more prevalent in the case of more violent pathogen by adapting standard methods developed in chemical expiratory events such as coughing and sneezing (20, 40). The engineering to describe the “continuously stirred tank reactor” ultimate fate of the droplets is determined by their size and the (49), as detailed in SI Appendix, section 1. We assume that the airflows they encounter (41, 42). Exhalation events are accom- droplet-borne pathogen remains airborne for some time before panied by a time-dependent gas-phase flow emitted from the being extracted by the room’s ventilation system, inhaled, or mouth that may be roughly characterized in terms of either con- sedimenting out. The fate of ejected droplets in a well-mixed tinuous turbulent jets or discrete puffs (20, 38, 43). The precise ambient is determined by the relative magnitudes of two speeds: form of the gas flow depends on the nature of the exhalation the settling speed of the drop in quiescent air, vs , and the ambi- event, specifically the time dependence of the flux of air expelled. ent air circulation speed within the room, va . Drops of radius Coughs and sneezes result in violent, episodic puff releases (20), r ≤ 100 µm and density ρd descend through quiescent air of while speaking and singing result in a puff train that may be density ρa and dynamic viscosity µa at the Stokes settling speed 2 well approximated as a continuous turbulent jet (38, 43). Even- vs (r) = 2∆ρgr /(9µa ), prescribed by the balance between grav- tually, the small droplets settle out of such turbulent gas flows. ity and viscous drag (50), where g is the gravitational acceleration In the presence of a quiescent ambient, they then settle to the and ∆ρ = ρd − ρa . floor; however, in the well-mixed ambient more typical of a ven- We consider a well-mixed room of area A, depth H , and tilated space, sufficiently small drops may be suspended by the volume V = HA with ventilation outflow rate Q and outdoor ambient airflow and mixed throughout the room until being air change rate (typically reported as air changes per hour, removed by the ventilation outflow or inhaled (SI Appendix, or ACH) λa = Q/V . Mechanical ventilation imposes an addi- section 1). tional recirculation flow rate Qr that further contributes to the Theoretical models of airborne disease transmission in closed, well-mixed state of the room, but alters the emergent drop well-mixed spaces are based on the seminal work of Wells (44) size distributions only if accompanied by filtration. The mean and Riley et al. (45), and have been applied to describe the air velocity, va = (Q + Qr )/A, prescribes the air mixing time, 2 spread of airborne pathogens including tuberculosis, measles, τa = H /va = H /(2Da ), where Da = va H /2 is the turbulent dif- influenza, H1N1, coronavirus (SARS-CoV) (12–16, 46, 47), and, fusivity defined in terms of the largest eddies (51, 52), those on most recently, the novel coronavirus (SARS-CoV-2) (17, 25). the scale of the room (53). The timescale of the droplet set- These models are all based on the premise that the space of tling from a well-mixed ambient corresponds to that through interest is well mixed; thus, the pathogen is distributed uniformly a quiescent ambient (51, 52, 54), as justified in SI Appendix, throughout. In such well-mixed spaces, one is no safer from section 1. Equating the characteristic times of droplet settling, airborne pathogens at 60 ft than 6 ft. The Wells–Riley model H /vs , and removal, V /Q, indicates a critical drop radius rc = p (13, 15) highlights the role of the room’s ventilation outflow 9λa H µa /(2g∆ρ) above which drops generally sediment out, rate Q in the rate of infection, showing that the transmission and below which they remain largely suspended within the room rate is inversely proportional to Q, a trend supported by data prior to removal by ventilation outflow. We here define air- on the spreading of airborne respiratory diseases on college borne transmission as that associated with droplets with radius campuses (48). The additional effects of viral deactivation, sed- r < rc . The relevant physical picture, of particles settling from a imentation dynamics, and the polydispersity of the suspended well-mixed environment, is commonly invoked in the contexts of droplets were considered by Nicas et al. (14) and Stilianakis stirred aerosols (51) and sedimentation in geophysics (54). The and Drossinos (16). The equations describing pathogen trans- additional effects of ventilation, particle dispersity, and pathogen port in well-mixed, closed spaces are thus well established and deactivation in the context of airborne disease transmission were have recently been applied to provide risk assessments for indoor considered by Nicas et al. (14), Stilianakis and Drossinos (16)

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(glycosy- water 50% bound r mucins at of time gel-forming amounts evaporation 10% comparable The to and proteins) 5 lated contain typically they a and (φ solutes water 0.5% 1 bound contain of typically volume which similar droplets, saliva 1), radius initial with droplet a of For size, quantities equilibrium 58). significant the (57, retain water and which bound hygroscopic pathogens, and typically including proteins, solutes, are carbohydrates, residual salts, of consist dissolved nuclei” “droplet resulting events approximately respiratory than most in emitted 38). those 23, radius (11, of of fraction those nificant here, interest of to than corresponds greater which rates 6/h, ventilation recommends now ASHRAE fara uu hikb sltl as little as by shrink mucus airway of fraction, and volume ity, solute initial the timescale, evaporation an of room a for Wuhan rates, in radius ventilation winter minimal in such height those with Even including (55). apartments, Chinese for of rate Engineers exchange λ air Air-Conditioning outdoor minimal and a recommend Refrigerating [ASHRAE]) Soci- Heating, (American of homes ety American for standards through Tradition- ventilation respiration. ally, leakage and to to motion as serve their lead through occupants well airflow Moreover, enhance will as joints. ventilation and doors, materials and Natural construction windows space: through enclosed some flows be an generally even will in that, there ventilation, noteworthy mixing forced is of It absence the room. in well-mixed the upon of built assumption be will models whose 18), (17, here. al. et Buonanno and udln olmtido ibretasiso fCOVID-19 of transmission airborne indoor limit to guideline A Bush and Bazant 0 a − h iin eoedatvtd(oifciu)a rate a at (noninfectious) deactivated become virions The droplets exhaled of suspension polydisperse a consider We less diameter with drops exhaled that argued (56) Wells In 0 = = √ 3 .5h au oprbet h vrg f03/ reported 0.34/h of average the to comparable value a 0.35/h, epoiejsicto o our for justification provide we 1, section Appendix, SI to .5µm 0.01 r H c θ 1 = 2 = 4 = ≈ .3 80% .1 .2 .I re ogadaantifciu aerosols, infectious against guard to order In µm. 12 × ,teei nascae rtcldo ieof size drop critical associated an is there m, 10 fteriiilsz 5) ovrey droplets Conversely, (58). size initial their of at s 100 −10 r 50 eq ileaoaebfr etig The settling. before evaporate will µm m = r .Teeifrne r consistent are inferences These µm. r 2 n eq c r sat /s τ d 0 5 = e (r < p = 3 RH ) r 10 .5 φ r 25 skont aysrnl with strongly vary to known is 0 n volume and s 2 r s /(1 .Te“ibre droplets “airborne” The µm. r ece ihn08s 0.8 within reached are µm /(θ agsfrom ranges ◦ < RH ≈ λ 5) ndyar(RH air dry In (58). C v n r ,cntu oeu to up lose thus can 1%), (1 − d c and hscnttt sig- a constitute thus , (r 1 RH sterltv humid- relative the is − − ) RH RH prvlm fair, of volume (per √ srahdover reached is ), 3 0. V where )), τ a einferred be can d 2 λ e (r v ≈ 1 = 4/3π = ) nrelative on since 40%, .2 sfor ms c λ φ λ v v s (r a (r r r  = 3 0 is ), ) . , lrvoe aito U-)(9 rceia disinfectants chemical or (69) either using (UV-C) (e.g. enhanced be radiation may ultraviolet rates for deactivation that viral with effective estimate coronavirus) Syndrome this Respiratory at of East consistency (Middle rough MERS-CoV the assume at note we h SARS-CoV-2, and for 1.1 data further of ing life half a iaindcsmyb noprtdb augmenting by incorporated be amount an may ducts tilation and fptoe upne ihndoso radius of drops to within droplets according filter suspended (73–76). to pathogen size masks drop of of of function ability a the as factor, for penetration accounts mask roughly that a introduce We time). where radius), rate radius stant of by droplets transported pathogen-laden exhales pathogen individuals radius of of radius) drops per number/volume cally, framework. this in included precip- characteristic electrostatic with as (72) such itators (22), devices filtration of types Other of ratings Reporting (MERV) Efficiency Value Minimum required have filters by air Ordinary characterized filtration that (HEPA) as Protection air (71) Environmental particulate States high-efficiency United defines the Agency that note We rate. fraction, Q and filtration droplet and specif- data, (25) existing al. by et bounded as Miller ically, rate follow deactivation the we treat SARS-CoV-2, for imentally h dependence the 5,5) o h aeo oainlsmlct,w en size- a define we simplicity, rate notational sedimentation of dependent sake to the ambient For corresponds well-mixed 54). a it (51, from sedimentation ventilation, of of models no case established Wells– the with the For suspension to 45). nonreacting reduces (44, it model filtration, Riley by removed nor deactivated where n ae.Tolmtn ae fEq. the of of radius, cases limiting particle Two Eq. on to rates. according ent speed evolves, size settling drop each the of population of flow dependence recirculation the the to in filtration drop of probability nrae as increases that so radius room. of quiescent a drop in a floor for to taken ceiling time from the of inverse the value, † aeof Rate change eednismgtb nlddi tagtowr fashion. these straightforward characterized, a reliably in once included that, be note but might (78), dependencies airflow of direction or (77) activity o h aeo ipiiy ed o osdrhr h eedneof dependence the here consider not do we simplicity, of sake the For r h nuneo i lrto n rpe etigi ven- in settling droplet and filtration air of influence The ese ocaatrz h concentration the characterize to seek We hnoeifce niiuletr oma time at room a enters individual infected one When 25 λ scmol xrse ntrso h rmr udo air outdoor primary the of terms in expressed commonly is , v RH H ◦ = and C v 2 λ C s O V v v s I (r = s 53 = Z (r 2 0 = 0 1 = (0) ∂ = , p P ) ∂ rmexhalation from rdcinrate Production = ) C O λ = t C stepril etigsedand speed settling particle the is (r Q RH f 3 ± n eciainmaue n1 at h 16 in measured deactivation [no (r (r Q r = Q (70). ) = ) P 0 = 11% b /(Q , = ) h aisrsle ahgnconcentration pathogen radius-resolved the , (r λ r t 79% = P I stebetigflwrt ehldvlm per volume (exhaled rate flow breathing the is Q = ) v easm htec of each that assume We . )/(λ rp fifiieia ieta r neither are that size infinitesimal of drops , (RH b p r n f 6) and (66)] + C λ (r d − c (r r 23 s Q ) )λ (r (r (68), = )V p where ), ± sntytwl hrceie exper- characterized well yet not is (Q )V r ) f Q − where ,  d 20 = 2 r p p (r 1 tarate a at ), + osrt rmvniain filtration ventilation, from rate Loss ◦ /V λ f f λ − eietto,addeactivation and sedimentation, and C https://doi.org/10.1073/pnas.2018995118 v )p > p ausof values s λ 1 = f (r e h eiclto o rate, flow recirculation The . to v m † 99. Q 1 −λ 0 = = ) Q h concentration, The (r r r fitrs.Frtecase the For interest. of are p nseicsz ranges. size specific in 90% .Fnly ent that note we Finally, .0/h. o eoo particles. aerosol for 97% c f + )c + ( (r RH h[orsodn to [corresponding .63/h r v λ v v ) s Q t v ) s (r (r 45  λ A r = eaigt steady a to relaxing , stepoaiiyof probability the is 65% = ) c )/H + stettlairflow total the is to (r P p nme/ieper (number/time λ f λ = ) = ,cnas be also can 70%, (r C v v = I r 0 = 0 V (r Q ) (t r PNAS λ λ < p hnevolves then s gi,the again, is, 6).Pend- (67)]. ) , ) osediment to m = a a .6RH t tdiffer- at 1, Q C p r (r nrespiratory on + ) infectious Q 22 m λ r tacon- a at /r (specifi- C λ v Owing . r (r | (r ± f 0 = c (r t f12 of 3 (r ) ) h ) 1 < 0 = 2 , + ) [1] −1 ◦ a , t by as 1, C ), , , ,

ENGINEERING λs (r) + λv (r). Note that both the equilibrium concentration and We define the airborne disease transmission rate, βa (t), as the the timescale to approach it are decreased by the combined mean number of transmissions per time per infectious individual effects of ventilation, air filtration, particle settling, and deac- per susceptible individual. One expects βa (t) to be proportional tivation (14, 64). Owing to the dependence of this adjustment to the quantity of pathogen exhaled by the infected person, and process on the drop size, one may understand it as a dynamic to that inhaled by the susceptible person. Gammaitoni and Nucci sifting process wherein larger droplets settle out and reach their (12) defined the airborne transmission rate as βa (t) = Qb ci Cs (t) equilibrium concentration relatively quickly. However, we note for the case of a population evolving according to the Wells– that, in the absence of filtration and deactivation (λf = λv = 0), Riley model and inhaling a monodisperse suspension. Here, ci −1 the adjustment time, λc , depends only weakly on drop size, is the viral infectivity, the parameter that connects the fluid varying from V /(2Q) for the largest airborne drops (with radius physics to the epidemiology, specifically, the concentration of rc ) to V /Q for infinitesimal drops. The sedimentation rate of suspended pathogen to the infection rate. We note its rela- the “airborne” droplets of radius r ≤ rc is thus bounded above tion to the notion of “infection quanta” in the epidemiological by the air exchange rate, λs (r) ≤ λa . The exhaled drop size dis- literature (44). Specifically, ci < 1 is the infection quanta per −1 tribution depends strongly on respiratory activity (11, 17, 38, 39); pathogen, while ci > 1 is the “infectious dose,” the number of thus, so too must the radius-resolved concentration of airborne aerosol-borne virions required to cause infection with probability pathogen. The predicted dependence on respiratory activity (11) 1 − e−1 = 63%. of the steady-state volume fraction of airborne droplets, φs (r) = For the polydisperse suspension of interest here, we define the Cs (r)/cv (r), is illustrated in Fig. 1. airborne transmission rate as

Fig. 1. Model predictions for the steady-state, droplet radius-resolved aerosol volume fraction, φs(r), produced by a single infectious person in a well-mixed room. The model accounts for the effects of ventilation, pathogen deactivation, and droplet settling for several different types of respiration in the absence 2 of face masks (pm = 1). The ambient conditions are taken to be those of the Skagit Valley Chorale superspreading incident (25, 27) (H = 4.5 m, A = 180 m , −1 −1 λa = 0.65 h , rc = 2.6 µm, λv = 0.3h , and RH = 50%). The expiratory droplet size distributions are computed from the data of Morawska et al. (ref. 11, 3 figure 3) at RH = 59.4% for aerosol concentration per log-diameter, using nd(r) = (dC/d log D)/(r ln 10). The breathing flow rate is assumed to be 0.5m /h for nose and mouth breathing, 0.75 m3/h for whispering and speaking, and 1.0m3/h for singing.

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P . ∼ 1 , C tri u oe,wihcnas eepesda h aeof rate the as expressed Eq. be person, in also infected equality an can by which emission model, quanta our in eter h nuneo oharfitainadptoe eciain we deactivation, pathogen Eq. and from filtration deduce, air rate, both exchange of influence air the the than less the on multiplying at humidity measured by were and analysis relative captured filtration, be of can air effect distribution exchange, size The air droplet deactivation. with associated viral rate cation where tt iutos htbud h uuaieepsr time exposure cumulative the bounds that (CET), situations, state exposure. of forms various in given oe 1,1,1,4) ob rcs,te nerdaquanta a inferred they precise, be To 45). Wells–Riley assumption 17, the the of 13, terms of Chorale (12, in Valley basis described model Skagit was the transmission the the on of that analysis (27), recent incident their superspreading in (25) improved al. et to lead so motivate and will data, attempt such an for more such estimates of that acquisition hope these the make the We transmissibility with strains. viral relative inferences and the populations that different by SARS-CoV-2, consider of rescale strain may original we the to for exposed Our value individuals COVID-19. baseline data a of epidemiological provide events inferences existing superspreading of early from basis gathered the Nevertheless, on for 85). estimates activities (92, (84, rough piratory making strains disease by viral the proceed different we of between progression (86– and during populations 93), individuals different between among widely 91), vary to expected are individual, transmissibility, infectious an relative by the quanta infection epi- exhaled the of is guideline our parameter, in demiological quantity constrained poorly only The COVID-19 to Application 75). a (74, masks by high-quality transmission of risk the factor reduce will persons susceptible and of risk as the person, increases infected susceptible infection the the of of inhalation exhalation the the and both individual of contagion flux exercis- of volume inhalation by the of on rate example, depends the Since for shouting. their or output, increase singing, to pathogen ing, as and where way rooms a rate in such respiration risk in greater themselves volume exerting at large are is people with One rooms rates. in ventilation safer high in and is periods minimize One extended To areas. spending populated avoid clear. highly should immediately one infection, is of which risk of interpretation the follows, what in see shall we As person. unfiltered the infected f in an that to of room breath well-mixed the in quanta infection factor, tion settings. p 3 d q yntn httesdmnainrt farsl susually is aerosols of rate sedimentation the that noting By etu riea ipegieie prpit o steady- for appropriate guideline, simple a at arrive thus We nifrneof inference An 0. rvdsavlal igotci sesn h eaiers of risk relative the assessing in diagnostic valuable a provides = 4/(1 R p 0 v ∞ m 2 s Eq. Appendix, SI − n = rmtcefc ie that given effect dramatic a , q RH f v (r d s ( = )dr C r ic h rpe itiuin sdi our in used distributions droplet the since ), 4 and ), q Q h atri h e ies-pcfi param- disease-specific key the is latter The . ensteefcieifciu rpradius drop infectious effective the defines oecnevtv on nteCET, the on bound conservative more a 5, b and (N /(λ C Q q N − c λ b s 2 970 = (¯ c  < τ r ieie ak onb ohinfected both by worn masks Likewise, . r  < 1)τ C h hr qaiydfie h dilu- the defines equality third The S7. = )V RH o ifrn ouain nvarious in populations different for q s λ r s h ai ftecnetainof concentration the of ratio the ), a Q h rdc fteconcentration the of product the , r 60% = quanta/m + eepaiethat emphasize We . b 2 https://doi.org/10.1073/pnas.2018995118 λ Q λ p λ λ c m a 2 b 2 f V s V p (¯ C (r r m 2 + q + ) (11). ) s C λ < p r v λ C 3 q m , s q s λ q A r a aeb Miller by made was ≤ v = a eeatfrelderly for relevant , C . (¯ n yneglecting by and , r 0.1 Q q ) b o ifrn res- different for stearpurifi- air the is C o moderately for s q r PNAS h second The . nodrto order in C q C | and q f12 of 5 and , r ¯ [5] [6] by s r r ,

ENGINEERING emission rate of λq = Cq Q¯ b = 970 quanta/h for a mean breathing of activity-dependent aerosol concentrations reported by Asadi 3 rate of Q¯ b = 1.0 m /h appropriate for singing (25). This inference et al. (38, 39). Specifically, we calculated the aerosol volume frac- is roughly consistent with studies of other related viral diseases. tions from the reported drop-size distributions (from figure 5 of 3 For example, Liao et al. (46) estimated Cq = 28 quanta/m from ref. 39) for a different set of expiratory activities that included the rate of indoor spreading of SARS-CoV, in a hospital and an various breathing patterns and speaking aloud at different vol- elementary school. Estimates of Cq for H1N1 influenza fall in the umes. We then used these volume fractions to rescale the value 3 3 range 15 to 128 quanta/m (47). For SARS-CoV-2, Buonanno Cq = 72 quanta/m for speaking at intermediate volume (39), 3 et al. (17) estimate a Cq range of 10.5 to 1,030 quanta/m , on which we chose to match the value inferred for the most similar the basis of the estimated infectivity ci = 0.01 to 0.1 of SARS- respiratory activity considered by Morawska et al. (11), specifi- CoV (94) and the reported viral loads in sputum (92, 93, 95), cally, voiced counting with pauses (11). Notably, the quanta con- and note that the precise value depends strongly on the infected centrations so inferred, Cq , are consistent across the full range of person’s respiratory activity. Notably, their range spans the high activities, from nasal breathing at rest (1 to 10 quanta/m3) to oral value inferred for the Skagit Valley Chorale (25), and all of our breathing and whispering (5 to 40 quanta/m3), to loud speaking inferences to follow. and singing (100 to 1,000 quanta/m3). We proceed by estimating quanta concentrations, Cq , or, Our inferences for Cq from a number of superspreading events equivalently, quanta emission rates, λq = Qb Cq , for different are also roughly consistent with physiological measurements of forms of respiration. First, we solve Eq. 1 to obtain the steady- viral RNA in the bodily fluids of COVID-19 patients at peak 3 state radius-resolved droplet volume fraction φs (r) for various viral load. Specifically, our estimate of Cq = 72 quanta/m for hypothetical expiratory activities in the room of the Skagit Val- voiced counting (11) and intermediate-volume speech (39) with 3 ley Chorale, using the drop size distributions of Morawska et al. integrated aerosol volume fractions φ1 = 0.36 and 0.11 (µm/cm) (11). Our results are shown in Fig. 1. Integrating each curve up corresponds, respectively, to microscopic concentrations of cq = 8 8 to the critical radius rc , we then obtain an activity-dependent vol- ci cv = 2 × 10 and 7 × 10 quanta/mL (see SI Appendix). Res- R rc ume fraction of infectious airborne droplets φ1 = 0 φs (r)dr in piratory aerosols mainly consist of sputum produced by the the choir room (see SI Appendix). Finally, we assume the inferred fragmentation (96) of mucous plugs and films in the bronchi- 3 value, Cq = 970 quanta/m , for the superspreading incident (25) oles and larynx (34–36). Larger droplets are thought to form that resulted from the expiratory activity most resembling singing by fragmentation of saliva in the mouth (36, 37). Airborne viral [voiced “aahs” with pauses for recovery (11)], and deduce val- loads are usually estimated from that of saliva or sputum (61, ues of Cq for other forms of respiration by rescaling with the 92, 93, 95, 97). After incubation, viral loads, cv , in sputum tend 8 11 appropriate φ1 values. Our predictions for the dependence of to peak in the range 10 to 10 RNA copies per milliliter (92, Cq on respiratory activity are shown in Fig. 2. For validation, we 93, 95), while much lower values have been reported for other also show estimates for Cq based on the recent measurements bodily fluids (92, 93, 98). Virus shedding in the pharynx remains

Fig. 2. Estimates of the “infectiousness” of exhaled air, Cq, defined as the peak concentration of COVID-19 infection quanta in the breath of an infected person, for various respiratory activities. Values are deduced from the drop size distributions reported by Morawska et al. (11) (blue bars) and Asadi et 3 al. (39) (orange bars). The only value reported in the epidemiological literature, Cq = 970 quanta/m , was estimated (25) for the Skagit Valley Chorale superspreading event (27), which we take as a baseline case (sr = 1) of elderly individuals exposed to the original strain of SARS-CoV-2. This value is rescaled R rc by the predicted infectious aerosol volume fractions, φ1 = 0 φs(r)dr, obtained by integrating the steady-state size distributions reported in Fig. 1 for different expiratory activities (11). Aerosol volume fractions calculated for various respiratory activities from figure 5 of Asadi et al. (39) are rescaled so that 3 the value Cq = 72 quanta/m for “intermediate speaking” matches that inferred from Morawska et al.’s (11) for “voiced counting.” Estimates of Cq for the outbreaks during the quarantine period of the Diamond Princess (26) and the Ningbo bus journey (28), as well as the initial outbreak in Wuhan City (2, 81), are also shown (see SI Appendix for details).

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(86–88), 100, that consider- rates (89–91, evidence have death values children growing and that is these hospitalization established rescale lower well is ably to It freedom strains. transmissibility viral the relative retain the by but universal, is of dependence (see debate some which of to subject 5). extent the section Appendix, remains the space being that well-mixed passengers note a the we with However, the consistent rest. value at a primarily (26), ship quarantined the cruise onboard event spreading the quanta/m naqitbs npriua,choosing particular, in bus; quiet a on uncer- the be Considering in capacity. might tainty to as filled speaking, bus intermediate a of onboard range expected the in infer pollutants lies thus that of We value (99). studies buses on transit based British windows, estimate in closed We with rate. bus exchange moving air the for except 2). that (Fig. with breathing assume apartment infer and thus typical (55), We ACH a 0.34 in the of persons before three 30 mean time the area of consider mean We size isolation. to patient household corresponds and symptoms it of onset that tenta- assuming time, then for may number, estimated (81), number transmission duction We outbreak reproduction of (32). Wuhan average 80% the homes the that people’s equate inference tively in the apartments, arose with assume family clusters we consistent in 81), is (2, predominantly as City occurred Wuhan spreading in that COVID-19 of characterized outbreak well of tial less values consistent slightly in roughly detailed of as number events, a trans- spreading indoor to for our applying support model crudely Further mission by 22). provided (4, is dominant hypothesis pandemic that the this COVID-19 evidence is the transmission 29) of airborne respiratory driver 28, indoor in that 23, infectious and extremely 19, aerosols and (5, present is epidemiological SARS-CoV-2 and 67) 66, a caused former the only that fact pandemic. the with consistent is virions), with SARS-CoV, than that infectious inference c more directly The times obtained 39). 10 (11, is inferences COVID-19 SARS-CoV-2 our for data below spreading magnitude from of order an ae npeiu neecsfrSR-o 9) Buonanno (94), SARS-CoV estimated (17) for al. inferences assuming et and previous load on viral this based contain Using (93), to milliliter. swabs likely per throat are in copies viral than aerosols Since sputum infectious mL). in most 3 greater the to 50% mL to 1 20 are (typically loads (92) swab throat reaches and per symptoms copies of week first the during high r i epoedb aigtesmlfigasmto htthe that assumption simplifying the making by proceed We o h igobsicdn,almdlprmtr r known are parameters model all incident, bus Ningbo the For 31, (3, virological emerging with consistent are findings Our ≈ 1 = imn Princess Diamond s 10% r h eaiessetblt faut ae 5yt 4y was y) 64 to y 15 (aged adults of susceptibility relative the , 23% = m λ 3 a netosds nteodro 0aerosol-borne 10 of order the on dose infectious (an a 2 ial,w ne au of value a infer we Finally, . n ih loifravlecnitn ihresting with consistent value a infer also might one , e esnadawne ero etlto rate ventilation bedroom winter a and person per s epoedb sn hs ausof values these using by proceed We . r C 68% = C q 30 = q R neprtr ciiyilsrtdi i.2 Fig. in illustrated activity expiratory on in c hl hto hlrn(gd0yt 4y) 14 to y 0 (aged children of that while , (τ q a eaeutl ecie ntrsof terms in described adequately be can quanta/m 2 = euse We ). × R C 10 q 0 s 7 r 3 = l fwihyield which of all Appendix, SI soni i.2.Frteini- the For 2). Fig. in (shown 3 au xetdfrnormal for expected value a , unam o SARS-CoV-2, for quanta/mL o ifrn g rusand groups age different for ihteido repro- indoor the with .3, τ λ λ 5 = a C v 0 = q 0 = .5 30 = C q hyields .34/h hand .3/h steexposure the as d 90 = imn Princess Diamond λ quanta/m a c 1 = v 7 quanta/m ≈ s × r . r ¯ hfra for 25/h 10 10 o these for 2 = C c 9 8 i 3 q 2% = RNA RNA from 57 = µm. 3 a , SI h edt iiietesaigo norsae maintain space, indoor of sharing the underscores it minimize Furthermore, to COVID-19 88). the need (86, of exam- elderly the This toll min. the devastating 18 could on the than occupants pandemic into more insight three no for provides state, room ple steady the mechanical in in remain the With ACH) safely case safe. 8 which marginally (at in only person, ventilation infected is transient an Rule the of for Fifteen-Minute arrival min min the 17 3 to after only response or after conditions, fails natural Rule quasi-steady For commu- Six-Foot under striking. the the is ACH), ventilation of (0.34 of ventilation effect vulnerability the of the again, tolerance Once reflect nity. a to and for chosen three guideline probability, ft of the 80 occupancy plot of maximum we area New minimum a in a requires recommends homes law nursing COVID-19 City, In of fraction (86–88). York large deaths a and of for hospitalizations order account which an facilities, by care limit collective time activity, the physical lower 2). (Fig. of would magnitude singing periods or Extended (C speech, norm. respiration a resting of the where assumption is 77), the stress, on (38, We COVID-19 based rare. classroom” for are be “quiet would time predictions transmissions our recovery school that and the however, d), than day, 14 would to per longer d ventilation time for (7 adequate indoor safe with of be masks h thus wearing 6 group Assuming school respectively. a h, 80 and 8 (p use mask bound, transient accord- the for ventilation, to h mechanical safe ing 1.2 with is h the 7.2 classroom and the masks, ventilation enters natural individual without infected our and an by after clear occupancy time made normal is use For mask guideline. and ventilation and adequate teacher, of tolerance, tance their risk and modest students a 19 choose of occupancy an for designed preexisting and age with (86–89). dramatically conditions the varies given of vulnerability which for the to population, CETs according tolerance judiciously critical chosen the be assessing that should In consistent stress rest. activities occupants we or respiratory populations, considered, speech mild settings quiet relatively both with in in of engaged that, value respiratory are assuming the and taking are demographics In we different (17). with levels of activity strongly choice vary conservative guide- to the our with illustrate existing quanta/m facil- to COVID-19 the reasonable care for and appear elder data line would the an from it settings and inferences literature, two classroom our in Considering the time ity. interest, exposure or particular estimat- in occupancy of guideline maximum our of the value ing the illustrating by proceed We Studies refine Case to used be estimates. initial then crude might necessarily which our our events, that spreading is from hope the data apply Our infer to fashion. sufficient to quantitative be attempts the a to in that prove may guideline indicate physio- 2 safety to Fig. independent in self-consistent from reported sufficiently values and are events data spreading logical indoor of set igo ih6%getrtasisblt n lvtdrs of risk elevated children. and among transmissibility infection greater United 60% the in with emerged Kingdom recently revise which to 85), (84, need 202012/01) the (VOC anticipate we However, studies. these SARS-CoV- case of our strain original in the 2 and groups age different three u nlsssud h lr o lel oe n long-term and homes elderly for alarm the sounds analysis Our classroom, American typical a to guideline our apply first We nsmay u neecsof inferences our summary, In s r ausfrnwvrlvrat,sc stelnaeB.1.1.7 lineage the as such variants, viral new for values 3 oee,w mhsz htti au sexpected is value this that emphasize we However, . m 0 = ,teebud r nrae rmtcly to dramatically, increased are bounds these .3), C q ilmtvt h olcino oesuch more of collection the motivate will Eq. Appendix, SI https://doi.org/10.1073/pnas.2018995118  10% = C q 2 and e esn nFg 3B, Fig. In person. per .Teimpor- The 3A). (Fig.   C 0 = saprmtrthat parameter a is vnwt cloth with Even S8. s q r 30 = .01 rmadiverse a from PNAS transmission quanta/m C | q q 30) = f12 of 7 30 = 3 ,

ENGINEERING A B

Fig. 3. The COVID-19 indoor safety guideline would limit the cumulative exposure time (CET) in a room with an infected individual to lie beneath the curves shown. Solid curves are deduced from the pseudo-steady formula, Eq. 5, for both natural ventilation (λa = 0.34/h; blue curve) and mechanical ventilation√ (λa = 8.0/h; red curve). Horizontal axes denote occupancy times with and without masks. Evidently, the Six-Foot Rule (which limits occupancy to Nmax = A/(6 ft)) becomes inadequate after a critical time, and the Fifteen-Minute Rule becomes inadequate above a critical occupancy. (A) A typical school classroom: 20 persons share a room with an area of 900 ft2 and a ceiling height of 12 ft (A = 83.6m2, V = 301 m3). We assume low relative transmissibility 2 3 (sr = 25%), cloth masks (pm = 30%), and moderate risk tolerance ( = 10%) suitable for children. (B) A nursing home shared room (A = 22.3m , V = 53.5m ) with a maximum occupancy of three elderly persons (sr = 100%), disposable surgical or hybrid-fabric masks (pm = 10%), and a lower risk tolerance ( = 1%) to reflect the vulnerability of the community. The transient formula, SI Appendix, Eq. S8, is shown with dotted curves. Other parameters are Cq = 30 3 3 quanta/m , λv = 0.3/h, Qb = 0.5m /h, and r = 0.5 µm.

adequate, once-through ventilation, and encourage the use of to a substantial risk of airborne infection in indoor spaces. Our face masks. study suggests that, whenever our CET bound (5) is violated In both examples, the benefit of face masks is immediately during an indoor event with an infected person, at least one −2 apparent, since the CET limit is enhanced by a factor pm , the transmission is likely, with probability . When the tolerance  inverse square of the mask penetration factor. Standard surgi- exceeds a critical value, all occupants of the room should be con- cal masks are characterized by pm = 1 to 5% (73, 74), and so sidered close contacts and so warrant testing. For relatively short allow the CET to be extended by 400 to 10,000 times. Even cloth exposures (λa τ  1) initiated when the index case enters the face coverings would extend the CET limit by 6 to 100 times for room, the transient bound should be considered (SI Appendix, hybrid fabrics (pm = 10 to 40%) or 1.5 to 6 times for single-layer section 2). fabrics (pm = 40 to 80%) (75). Our inference of the efficacy of We proceed by considering the implications of our guide- face masks in mitigating airborne transmission is roughly consis- line for the implementation of quarantining and testing. While tent with studies showing the benefits of mask use on COVID-19 official quarantine guidelines emphasize the importance of iso- transmission at the scales of both cities and countries (22, 33, 83). lating infected persons, our study makes clear the importance of Air filtration has a less dramatic effect than face mask use in isolating and clearing infected indoor air. In cases of home quar- increasing the CET bound. Nevertheless, it does offer a means antine of an infected individual with healthy family members, of mitigating indoor transmission with greater comfort, albeit at our guideline provides specific recommendations for mitigating greater cost (22, 72). Eq. 5 indicates that even perfect air filtra- indoor airborne transmission. For a group sharing an indoor tion, pf = 1, will only have a significant effect in the limit of highly space intermittently, for example, office coworkers or classmates, recirculated air, Zp  1. The corresponding minimum outdoor regular testing should be done with a frequency that ensures airflow per person, Q/Nmax, should be compared with local stan- that the CET between tests is less than the limit set by the dards, such as 3.8 L/s per person for retail spaces and classrooms guideline. Such testing would become unnecessary if the time and 10 L/s per person for gyms and sports facilities (72). In the limit set by the CET bound greatly exceeds the time taken for above classroom example with a typical primary outdoor air frac- an infected person to be removed from the population. For tion of Zp = 20% (22), the air change rate λa could effectively the case of a symptomatic infected person, this removal time be increased by a factor of 4.6 by installing a MERV-13 filter, should correspond to the time taken for the onset of symp- pm = 90%, or a factor of 5.0 with a HEPA filter, pm = 99.97%. toms (∼5.5 d). To safeguard against asymptomatic individuals, At high air exchange rates, the same factors would multiply the one should use the recovery time (∼14 d) in place of the CET bound. removal time. Next, we illustrate the value of our guideline in contact trac- Finally, we briefly discuss how the prevalence of infection in ing (82), specifically, in prescribing the scope of the testing of the population affects our safety guideline. Our guideline sets a people with whom an infected index case has had close contact. limit on the indoor reproductive number, the risk of transmis- The CDC presently defines a COVID-19 “close contact” as any sion from a single infected person in the room. It thus implicitly encounter in which an individual is within 6 ft of an infected per- assumes that the prevalence of infection in the population, pi , son for more than 15 min. Fig. 3 makes clear that this definition is relatively low. In this low-pi limit, the risk of transmission may grossly underestimate the number of individuals exposed increases with the expected number of infected persons in the

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(20, cm 10 C of order at the behaved on typically well jet, the of origin virtual hs xrsin for expressions These = (0) nawl-ie om h encnetaino pathogen of concentration mean the room, well-mixed a In turbu- of form geometric simple relatively the of basis the On situa- other to guideline our apply to how on instructions For hr,b pcfigagvnro geometry, room given a specifying by There, Appendix. SI α = t C x 0 α Np A . Np t nraiglnal ihdistance with linearly increasing m ≈ i n h oeac hudb oee npropor- in lowered be should tolerance the and , i ≈ 0.1 C fi xed n.Cnesl,when Conversely, one. exceeds it if x cm 2 0 = = to r ie yreplacing by given are 0 f C v d 0.15 < (x q 2 and ) isi h ag f000 o00.With 0.01. to 0.0001 of range the in lies /c r c eoe h rs-etoa rao the of area cross-sectional the denotes v ntecs hr h nieyo the of entirety the where case the in ) stetpcljtetanetcoefficient entrainment jet typical the is v steehldptoe concentration. pathogen exhaled the is C f (x (x d r ai ntelmtof limit the in valid are ) ≤ = ) f λ d c Q = (r M b Q ) /Q 1/2 λ > b x /(λ with o yia om n air and rooms typical For . /(α a c = f C x (¯ d t r + C j Q x )V (x x √ 0 /V v o xml,i the in example, For . x n omlzn uhthat such normalizing and , )/C πρ fapproximately of ), h iuinfac- dilution the , rmtesource, the from x a > 0 Concurrently, ). = x M v Np where , A = m 1/2 i → πρ /(α x the 0, a v r sthe is t 2 x v ), 2 § rmteabetb noewti h omatratime a after room inhaled the be within would anyone V by infected pathogen an ambient of by the exhaled amount from air equivalent of full An lung person. a ingests directly person a than risk greater ambient. substantially of well-mixed a absence the pose the may in jets Thus, respiratory dimension. masks, room for characteristic m the 10 than exceeds distance This ambient. the f of that to reduced is A ftasiso rmrsiaoyjt,a eue yYn tal. et Yang factor by the deduced from as aside jets, (106), respiratory from transmission Eq. of from Substitution ft. 6 set 5 as further such distance, may interperson one allowed imposed, is distancing expects one in jets reducing respiratory of by risk environment C thus the distanced could against socially guideline safeguard a Our to probability. adopted transmission be the of tion room, well-mixed the of C that to relative concentration pathogen ,dpneto geometry, on dependent [7], is as be, transmission will airborne plumes short-range respiratory against by mitigate to intended another. each face they time the of and If fraction table, the a across to distance correspond the to roughly correspond both for made be may p estimates meaningful instances, certain In greatest. necessarily is infection deduce of thus risk We the which between bors, infected the by of denote plume and respiratory person, the by in denote lies neighbor We susceptible [5]. (p guideline worn safety being our when not appropriate are transmission, masks plume short-range of risk tional conservative less a for allow of the would choice of which fraction of encounter small some consideration to for time, expect only would plume respiratory one infected setting, circulating an a indoor with an generally, in in More arise population (103). may airplane as directly or individual, classroom infected seated an a a is of describes plume individual respiratory scenario susceptible the worst-case in a latter where the situation that static note We 0.01. to ft, (when 6 than ambient associ- higher of well-mixed The times the (43). f distance 30 in 3% roughly a concentration of still steady-state factor is at the jet a jet the by in directly diluted turbulent concentration is is ated infected jet person an the susceptible which of a over path which the in Rule, in Six-Foot is the plume by respiratory a with encounter τ risk close greater worst-case a is this transmission than which airborne for which room, beyond time choir critical Skagit the of geometry the concentration jet per- infected infected the an Since period. C with extended or room an an a episodic for and son sharing jet, (either to with respiratory encounter risk associated individual’s dilution relative close exposure infected the the a an assess with and of now prolonged) person room may susceptible we well-mixed jets, a the respiratory of of rate factor dilution the d d j j j 1 = b m 1/2 eel httescn emi Eq. in term second the that reveals (6ft efis osdrawrtcs,coecnatseai nwhich in scenario close-contact worst-case, a consider first We emytu aearltvl rd siaefrteaddi- the for estimate crude relatively a make thus may We N 0 = nteaoeetoe ag n oi yial uhgreater much typically is so and range aforementioned the in (x (x and /(Q /(α )/(f ) cuat r ragdrnol na norsae then space, indoor an in randomly arranged are occupants .0 ,ads ol euti omnuaeamplifica- commensurate a in result would so and .001), )/(f erae ihdsac rmissuc,oemyass its assess may one source, its from distance with decreases b x f .W etcnie h os-aeseai governed scenario worst-case the consider next We h. o xml,i opednsa restaurant, a at dines couple a if example, For . t d d f . d where ), C d C eodwihteptoe ocnrto ntejet the in concentration pathogen the which beyond ), 0 p 0 = ) j hc s3t 0 for 300 to 3 is which ), tan = A m 1/2 R V −1 in b /(α (τ ≈ x α > t ) 500 t /π f " d 0 + 1 x p h itnebtennaetneigh- nearest between distance the and hr stu rtcldistance, critical a thus is There ). Li h oueprbet.For breath. per volume the is mL j m ent htaysc guideline such any that note We . N 1 = https://doi.org/10.1073/pnas.2018995118 p x s j f A = d ,b digacreto to correction a adding by ), m 1/2 α p t f 7 x d A/N p # orsod oterisk the to corresponds j nterneo 0.0001 of range the in . < h rbblt hta that probability the hnsrc social strict When . x oteminimum the to  f yafco of factor a by d PNAS 0 = p . x the 001, j | would would f12 of 9 τ [7] =

ENGINEERING flow, and human behavior, while our guideline for the mitigation and long-range airborne transmission leads to a guideline of the of long-range airborne transmission [5] is universal. form of Eq. 7 that would bound both the distance between occu- We note that the use of face masks will have a marked effect pants and the CET. Circumstances may also arise where a room on respiratory jets, with the fluxes of both exhaled pathogen and is only partially mixed, owing to the absence or deficiency of air momentum being reduced substantially at their source. Indeed, conditioning and ventilation flows, or the influence of irregu- Chen et al. (42) note that, when masks are worn, the primary larities in the room geometry (107). For example, in a poorly respiratory flow may be described in terms of a rising thermal ventilated space, contaminated warm air may develop beneath plume, which is of significantly less risk to neighbors. With a the ceiling, leading to the slow descent of a front between population of individuals wearing face masks, the risk posed by relatively clean and contaminated air, a process described by respiratory jets will thus be largely eliminated, while that of the “filling-box” models (107). In the context of reducing COVID- well-mixed ambient will remain. 19 transmission in indoor spaces, such variations from well Finally, we stress that our guideline is based on the average mixedness need be assessed on a room-by-room basis. Nev- concentration of aerosols within the room. For every region of ertheless, the criterion [5] represents a minimal requirement enhanced airborne pathogen concentration, there is necessarily for safety from long-range airborne infection in well-mixed, a region of reduced concentration and lower transmission risk indoor spaces. elsewhere in the room. The ensemble average of the transmis- We emphasize that our guideline was developed specifically sion risk over a number of similar events, and the time-averaged with a view to mitigating the risk of long-range airborne trans- transmission risk in a single event, are both expected to approach mission. We note, however, that our inferences of Cq came that in the well-mixed steady state, as in ergodic processes in from a number of superspreading events, where other modes statistical mechanics. This feature of the system provides ratio- of transmission, such as respiratory jets, are also likely to have nale for the self-consistency of our inferences of Cq , based on contributed. Thus, our estimates for Cq are necessarily overesti- the hypothesis of the well-mixed room, from the diverse set of mates, expected to be higher than those that would have arisen spreading events considered herein. from purely long-range airborne transmission. Consequently, our safety guideline for airborne transmission necessarily pro- Discussion and Caveats vides a conservative upper bound on CET. We note that the We have focused here primarily on airborne transmission, for additional bounds required to mitigate other transmission modes which infection arises through inhalation of a critical quantity of will not be universal; for example, we see, in Eq. 7, that the dan- airborne pathogen, and neglected the roles of both contact and ger of respiratory jets will depend explicitly on the arrangement large-drop transmission (6). While motivated by the COVID-19 of the room’s occupants. Finally, we reiterate that the wearing of pandemic, our theoretical framework applies quite generally to masks largely eliminates the risk of respiratory jets, and so makes airborne respiratory illnesses, including influenza. Moreover, we the well-mixed room approximation considered here all the more note that the approach taken, coupling the droplet dynamics to relevant. the transmission dynamics, allows for a more complete descrip- Our theoretical model of the well-mixed room was developed tion. For example, consideration of conservation of pathogen specifically to describe airborne transmission between a fixed allows one to calculate the rate of pathogen sedimentation and number of individuals in a single well-mixed room. Nevertheless, associated surface contamination, consideration of which would we note that it is likely to inform a broader class of transmission allow for quantitative models of contact transmission and so events. For example, there are situations where forced ventila- inform cleaning protocols. tion mixes air between rooms, in which case the compound room Typical values for the parameters arising in our model are becomes, effectively, a well-mixed space. Examples considered listed in SI Appendix, Table S1. Respiration rates Qb have been here are the outbreaks on the Diamond Princess and in apart- 3 measured to be ∼ 0.5 m /h for normal breathing, and may ments in Wuhan City (see SI Appendix); others would include increase by a factor of 3 for more strenuous activities (17). prisons. There are many other settings, including classrooms and Other parameters, including room geometry, ventilation, and factories, where people come and go, interacting intermittently filtration rates, will obviously be room dependent. The most with the space, with infected people exhaling into it, and suscepti- poorly constrained parameter appearing in our guideline is Cq sr , ble people inhaling from it, for limited periods. Such settings are the product of the concentration of pathogen in the breath of also informed by our model, provided one considers the mean an infected person and the relative transmissibility. The latter, population dynamics, and so identifies N with the mean number sr , was introduced in order to account for the dependence of of occupants. transmissibility on the mean age of the population (86–88, 91) The guideline [5] depends on the tolerance , whose value in a and the viral strain (84, 85). The value of Cq sr was inferred particular setting should be set by the appropriate policy makers, from the best characterized superspreading event, the Skagit informed by the latest epidemiological evidence. Likewise, the Valley Chorale incident (25), as arose among an elderly pop- guideline includes the relative transmissibility sr of a given viral ulation with a median age of 69 y (27), for which we assign strain within a particular subpopulation. These two factors may sr = 1. The Cq value so inferred was rescaled using reported be eliminated from consideration by using [6] to assess the rela- drop size distributions (11, 23, 38) allowing us to estimate Cq tive behavioral risk posed to a particular individual by attending for several respiratory activities, as listed in Fig. 3. Further com- a specific event of duration τ with N other participants. We thus parison with inferences based on other spreading events of new define a relative risk index, viral strains among different populations would allow for refine- 2 2 ment of our estimates of Cq and sr . We thus appeal to the N τCq Qb pm IR = , [8] public health community to document the physical conditions λa V enumerated in SI Appendix, Table S1 for more indoor spreading events. that may be evaluated using appropriate Cq and Qb values (listed Adherence to the Six-Foot Rule would limit large-drop trans- in SI Appendix, Table S2). One’s risk increases linearly with the mission, and adherence to our guideline, Eq. 5, would limit number of people in a room and duration of the event. Rela- long-range airborne transmission. We have also shown how the tive risk decreases for large, well-ventilated rooms and increases sizable variations in pathogen concentration associated with res- when the room’s occupants are exerting themselves or speak- piratory flows, arising in a population not wearing face masks, ing loudly. While these results are intuitive, the approach taken might be taken into account. Consideration of both short-range here provides a physical framework for understanding them

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Transmission Manatunge, 8. J. Gunawardana, COVID-19. B. of Perera, physics H. flow The Jayaweera, Seo, M. J.-H. Ni, 7. R. the Mittal, face R. should world 6. The COVID-19. SARS-CoV-2: of of transmission transmission Airborne airborne Cao, address J. Morawska, to L. time is 5. It Milton, K. D. Morawska, L. 4. Lednicky A. J. 3. Li Q. 2. Chen N. 1. bv l,orsuymkscerteiaeuc fteSix- the of inadequacy the clear makes study our all, Above (2020). 2020. March Washington, County, (2020). 2020. February–March worldwide, event. superspreading Chorale Valley Skagit the subjects. human healthy of sneezing. and coughing enough. be (2020). not could distance personal infection. SARS-CoV-2 of transmission assessment. risk infection for (2020). SARS-CoV-2 of rate emission droplets. respiratory spaces. enclosed in infections airborne (2005). epidemiological alternative of review analytical An models. spaces: confined in tuberculosis measures. control TB activities. expiratory during tract respiratory human (2020). 4062 11, walking. by resuspended dust in infection? aerosols. and droplets by virus reality. Dis. Infect. Clin. patients. pneumonia. infected study. descriptive A China: (2020). Wuhan, in pneumonia coronavirus eoos osCVD1 rnmtvaeprtr particles? expiratory (2020). via 635–638 transmit COVID-19 Does aerosols: COVID-19. of spread the (2020). 14857–14863 for route dominant the as pathogens. respirable of Emission infection: airborne al rnmsindnmc nWhn hn,o oe coronavirus– novel of China, Wuhan, in dynamics transmission Early al., et nio.Int. Environ. ibretasiso ot fCVD1:Wy2mtr/ to inter- of ft meters/6 2 Why COVID-19: of route transmission Airborne al., et nunaAvrsi rnmsil i eooie fomites. aerosolized via transmissible is virus A Influenza al., et n.J uecl ugDis. Lung Tubercul. J. Int. pdmooia n lnclcaatrsiso 9csso 09novel 2019 of cases 99 of characteristics clinical and Epidemiological al., et n.J net Dis. Infect. J. Int. norAir Indoor rnmsino ASCV2b naaino eprtr eoo in aerosol respiratory of inhalation by SARS-CoV-2 of Transmission al., et ibretasiso fSARS-CoV-2. of transmission Airborne al., et iedsrbto n ie foii fdolt xeldfo the from expelled droplets of origin of sites and distribution Size al., et ibeSR-o- ntearo optlro ihCOVID-19 with room hospital a of air the in SARS-CoV-2 Viable al., et 3121 (2020). 2311–2313 71, 070(2020). 105730 139, .R o.Interface Soc. R. J. mr.Ifc.Dis. Infect. Emerg. .Eg.J Med. J. Engl. N. 3–4 (2006). 335–347 16, .FudMech. Fluid J. 7–8 (2020). 476–482 100, .ArslMed. Aerosol J. nio.Res. Environ. norAir Indoor 0512 (2003). 1015–1026 7, MR ob otl ky Rep. Wkly. Mortal. Morb. MMWR. MR ob otl ky Rep. Wkly. Mortal. Morb. MMWR. 1910 (2020). 1199–1207 382, nio.Int. Environ. 3–6 (2014). 537–563 745, pdmo.Infect. Epidemiol. 3516 (2010). 1355–1366 7, 3 (1997). 335 3, n.J nio.Rs ul Health Publ. Res. Environ. J. Int. 0–1 (1997). 105–116 10, 2–4 (2015). 428–440 25, 089(2020). 109819 188, norAir Indoor 012(2020). 106112 145, .ArslSci. Aerosol J. rc al cd c.U.S.A. Sci. Acad. Natl. Proc. .Oc n.Hygiene Env. Occ. J. .FudMech. Fluid J. Science 0219 (2006). 1082–1091 134, 1–2 (2020). 314–323 31, nio.Int. Environ. eoo.Si Technol. Sci. Aerosol. Lancet 0–0 (2020). 303–304 370, 5–6 (2009). 256–269 40, 2(2020). F2 894, a.Commun. Nat. 507–513 395, 347–352 69, 606–610 69, 105794 141, 143–154 2, 2932 17, 117, 54, 3 .C Cheng K.-C. 53. aerosol. stirred a of deposition and coagulation The Pendlebury. D. E. Corner, J. 51. Deen, M. W. 50. Davis, J. R. Davis, E. M. 49. dynamic estimated transmission infection transmission Zhu airborne S. indoor of probabilistic 48. Risk suburban Milton, A K. a D. Rudnick, in Liang, N. S. measles H.-M. 47. of Chang, spread C.-F. Airborne Riley, Liao, L. R. C.-M. Murphy, 46. G. Riley, C. E. 45. jet-like produce can Speech Wells, F. Stone, W. A. 44. H. Fan, Y. Xue, N. Mendez, dominates S. route Abkarian, airborne in M. Short-range size Li, 43. Y. particle Yen, of H.-L. role Wei, J. The Zhang, Rawlinson, N. D. Chen, W. W. McLaws, 42. M.-L. Tovey, sneeze E. of Gralton, Visualization Bourouiba, J. L. 41. Bush, M. W. J. Techet, H. A. Scharfman, E. B. 40. Asadi S. 39. formation. Johnson aerosol G. breath of 36. mechanism The Morawska, L. Johnson, R. mechanics. D. frame- fluid modelling Respiratory 35. Grotberg, A B. Colvin, J. J. Gilligan, 34. A. C. Bradley, M. Retkute, R. Stutt, H. J. O. R. 33. Qian H. 32. Santarpia L. J. COVID-19 of 31. transmission aerosol Possible Heo, J. Bumjo, O. Chang, H. J. Hwang, E. S. 30. Nishiura H. 29. Shen Y. 28. 2 .C .Li .W aaof oeigido atcedpsto rmtruetflow turbulent from deposition particle indoor Modeling Nazaroff, W. W. Lai, K. C. A. 52. Asadi S. speech: 38. during filaments saliva of break-up and Stretching Stone, A. H. Abkarian, M. 37. oasa esOsn ooaRso,adRniZagfrimportant for Lidia Zhang Renyi Keating, and David Daniel Rossol, Hofmann, Bourouiba, Monona references. Lydia Olson, Kyle Bazant, Nels Hampden-Smith, Morawska, Lesley Mark and Cogswell, data, experimental sharing ACKNOWLEDGMENTS. information. supporting Availability. Data is study our in arising terms in of the presented glossary enable A (108). also is guideline spreadsheet safety guideline CO and safety from app data our of The use on (102). based set- available app indoor also online particular any convenient for A limit ting. CET the evaluating of means safety our of refinements guideline. quantitative to so and thereof estimates poie simple a provides S1 Dataset in included spreadsheet The iae eiecs soito ftruetdfuincefiin iharcag rate. change air Technol. with Sci. coefficient Environ. diffusion turbulent of Association residences: tilated 2012). Corporation, Maryland. Park, College in halls (2020). residence college in rates risks. concentration. dioxide infection carbon from airborne indoor assess (2005). to model school. elementary Infections virus. of (2020). 25237–25245 spreading 117, asymptomatic to relevant transport contact. close during (2020). infection respiratory of exposure review. A transmission: pathogen aerosolised droplets. respiratory to leading (2016). fragmentation fluid of Steps ejecta: speech. human during Deliv. Drug Pulm. Med. lock-down with combination in pandemic. facemasks COVID-19 of the effectiveness managing likely in the assess to work (2020). (Accessed https://doi.org/10.1101/2020.07.13.20041632 2020). August (2020). 1 [Preprint] medRxiv Korea. South Seoul, (2020). in 73–76 apartment 104, an in outbreak an with associated https://doi.org/10.1101/ (2020). 2020). [Preprint] July medRxiv 1 (Accessed (COVID-19). 2020.02.28.20029272 2019 disease avirus nosot surfaces. smooth onto B Soc. Phys. loudness. voice with mitigation. potential its (2020). and 102301 aerosolization pathogen for route A (2011). 839–851 42, China. eastern in riders bus etlto n aoaoycnre ct eprtr neto (ARI) infection respiratory acute confirmed laboratory and Ventilation al., et omnt ubekivsiaino ASCV2tasiso among transmission SARS-CoV-2 of investigation outbreak Community al., et feto ocn n riuainmne narslpril emission particle aerosol on manner articulation and voicing of Effect al., et eoo msinadsprmsindrn ua pehincrease speech human during superemission and emission Aerosol al., et nortasiso fSARS-CoV-2. of transmission Indoor al., et HradUiest rs,1955). Press, University (Harvard oaiyo ua xie eoo iedistributions. size aerosol expired human of Modality al., et 4,1951. 645, 64, lsdevrnet aiiaescnaytasiso fcoron- of transmission secondary facilitate environments Closed al., et oeigepsr ls oarpluinsucsi aual ven- naturally in sources pollution air to close exposure Modeling al., et ibreCnainadArHgee nEooia td fDroplet of Study Ecological An Hygiene: Air and Contagion Airborne nlsso rnpr Phenomena Transport of Analysis al S3. Table Appendix, SI h netosntr fptetgnrtdSR-o- aerosol. SARS-CoV-2 patient-generated of nature infectious The al., et m .Epidemiol. J. Am. l td aaaeicue nteatceand article the in included are data study All c.Rep. Sci. 0642 (2011). 4016–4022 45, .ArslSci. Aerosol J. lSOne PloS 2–3 (2009). 229–237 22, 2 etakWlimRsepr n iaAaifor Asadi Sima and Ristenpart William thank We udmnaso hmclRato Engineering Reaction Chemical of Fundamentals esr 4)t mrv h cuayo the of accuracy the improve to (47) sensors AAIt Med. Int. JAMA 38(2019). 2348 9, 0269(2020). e0227699 15, norAir Indoor 6–7 (2000). 463–476 31, 2–3 (1978). 421–432 107, rc .Sc A. Soc. R. Proc. https://doi.org/10.1073/pnas.2018995118 hs Fluids Phys. 6517 (2020). 1665–1671 180, .Infect. J. Ofr nvriyPes d ,2011). 2, ed. Press, University (Oxford 3–4 (2003). 237–245 13, 0036(2020). 20200376 476, norAir Indoor –3(2011). 1–13 62, 231(2011). 021301 23, ikAnal. Risk ul.Environ. Build. rc al cd c.U.S.A. Sci. Acad. Natl. Proc. nio.Int. Environ. 10.1111/ina.12766 , PNAS hs e.Fluids Rev. Phys. n.J net Dis. Infect. J. Int. x.Fluid Exp. 1097–1107 25, .ArslSci. Aerosol J. 106859 176, 105537 137, | .Aerosol J. 1o 12 of 11 (Courier 24 57, Proc. 5,

ENGINEERING 54. D. Martin, R. Nokes, Crystal settling in a vigorously converting magma chamber. 82. L. Ferretti et al., Quantifying SARS-CoV-2 transmission suggests epidemic control with Nature 332, 534–536 (1988). digital contact tracing, Science 368, eabb6936 (2020). 55. J. Hou et al., Air change rates in urban Chinese bedrooms. Indoor Air 29, 828–839 83. Y. Li, R. Zhang, J. Zhao, M. J. Molina, Understanding transmission and intervention for (2019). the COVID-19 pandemic in the United States. Sci. Total Environ. 748, 141560 (2020). 56. W. F. Wells et al., On air-borne infection. Study II. droplets and droplet nuclei. Am. J. 84. N. G. Davies et al., Estimated transmissibility and severity of novel SARS-CoV-2 variant Hyg. 20, 611–618 (1934). of concern 202012/01 in England. Science, 10.1126/science.abg3055 (2021). 57. X. Xie, Y. Li, A. T. Y. Chwang, P. L. Ho, W. H. Seto, How far droplets can move in indoor 85. Erik. Volz et al., Transmission of SARS-CoV-2 lineage B.1.1.7 in England: Insights from environments—Revisiting the wells evaporation–falling curve. Indoor Air 17, 211–225 linking epidemiological and genetic data. medRxiv [Preprint] (2021). https://doi.org/ (2007). 10.1101/2020.12.30.20249034 (Accessed 5 January 2021). 58. R. R. Netz, Mechanisms of airborne infection via evaporating and sedimenting 86. S. Richardson et al., Presenting characteristics, comorbidities, and outcomes among droplets produced by speaking. J. Phys. Chem. B 124, 7093–7101 (2020). 5700 patients hospitalized with COVID-19 in the New York City area. J. Am. Med. 59. J. V. Fahy, B. F. Dickey, Airway mucus function and dysfunction. N. Engl. J. Med. 363, Assoc. 323, 2052–2059 (05 2020). 2233–2247 (2010). 87. N. G. Davies et al., Age-dependent effects in the transmission and control of COVID- 60. D. K. Milton et al., Influenza virus aerosols in human exhaled breath: Particle size, 19 epidemics. Nat. Med. 26, 1205–1211 (2020). culturability, and effect of surgical masks. PLoS Pathog. 9, e1003205 (2013). 88. S. Garg, Hospitalization rates and characteristics of patients hospitalized with 61. R. Wolfel¨ et al., Virological assessment of hospitalized patients with COVID-2019. laboratory-confirmed coronavirus disease 2019: COVID-NET, 14 states, March 1–30, Nature 581, 465–469 (2020). 2020. MMWR. Morb. Mortal. Wkly. Rep. 69, 458–464 (2020). 62. L. C. Marr, J. W. Tang, J. Van Mullekom, S. S. Lakdawala, Mechanistic insights into the 89. Y. Zhu et al., A meta-analysis on the role of children in SARS-CoV-2 in household effect of humidity on airborne influenza virus survival, transmission and incidence. J. transmission clusters. Clin. Infect. Dis., 10.1093/cid/ciaa1825 (2020). R. Soc. Interface 16, 20180298 (2019). 90. A. P. S. Munro, S. N. Faust, Children are not COVID-19 super spreaders: Time to go 63. G. J. Harper, Airborne micro-organisms: Survival tests with four viruses. Epidemiol. back to school. Arch. Dis. Child. 105, 618–619 (2020). Infect. 59, 479–486 (1961). 91. M. Riediker, L. Morawska, Low exhaled breath droplet formation may explain 64. W. Yang, L. C. Marr, Dynamics of airborne influenza a viruses indoors and dependence why children are poor SARS-CoV-2 transmitters. Aerosol. Air Q. Res. 20, 1513–1515 on humidity. PloS One 6, e21481 (2011). (2020). 65. K. Lin, L. C. Marr, Humidity-dependent decay of viruses, but not bacteria, in aerosols 92. R. Wolfel¨ et al., Virological assessment of hospitalized patients with COVID-2019. and droplets follows disinfection kinetics. Environ. Sci. Technol. 54, 1024–1032 (2019). Nature 581, 465–469 (2020). 66. A. C. Fears et al., Comparative dynamic aerosol efficiencies of three emergent 93. Y. Pan, D. Zhang, P. Yang, L. L. M. Poon, Q. Wang, Viral load of SARS-CoV-2 in clinical coronaviruses and the unusual persistence of SARS-CoV-2 in aerosol suspensions. samples. Lancet Infect. Dis. 20, 411–412 (2020). medRxiv [Preprint] (2020). https://doi.org/10.1101/2020.04.13.20063784 (Accessed 15 94. T. Watanabe, T. A. Bartrand, M. H. Weir, T. Omura, C. N. Haas, Development of a dose- July 2020). response model for SARS coronavirus. Risk Anal. 30, 1129–1138 (2010). 67. N. Van Doremalen et al., Aerosol and surface stability of SARS-CoV-2 as compared 95. K. K.-W. To et al., Temporal profiles of viral load in posterior oropharyngeal with SARS-CoV-1. N. Engl. J. Med. 382, 1564–1567 (2020). saliva samples and serum antibody responses during infection by SARS-CoV-2: An 68. O. V. Pyankov, S. A. Bodnev, O. G. Pyankova, I. E. Agranovski, Survival of aerosolized observational cohort study. Lancet Infect. Dis. 20, 565–574 (2020). coronavirus in the ambient air. J. Aerosol Sci. 115, 158–163 (2018). 96. E. Villermaux, Fragmentation versus cohesion. J. Fluid Mech. 898, P1 (2020). 69. F. J. Garc´ıa de Abajo et al., Back to normal: An old physics route to reduce SARS-CoV-2 97. L. Zheng, J. Xu, F. Wu, W. Xu, Z. Long, Influences of ventilation modes on the coughing transmission in indoor spaces. ACS Nano 14, 7704–7713 (2020). droplet dispersion process in a cruise cabin. Chinese J. Ship Res. 11, 2 (2016). 70. A. Schwartz et al., Decontamination and reuse of N95 respirators with hydrogen per- 98. S. Zheng et al., Viral load dynamics and disease severity in patients infected with oxide vapor to address worldwide personal protective equipment shortages during SARS-CoV-2 in Zhejiang province, China, January-March 2020: Retrospective cohort the SARS-CoV-2 (COVID-19) pandemic. Applied Biosafety 25, 67–70 (2020). study. Br. Med. J. 369, m1443 (2020). 71. E. S. Mousavi, K. J. G. Pollitt, J. Sherman, R. A. Martinello, Performance analysis of 99. W. W. Song, M. R. Ashmore, A. C. Terry, The influence of passenger activities on portable HEPA filters and temporary plastic anterooms on the spread of surrogate exposure to particles inside buses. Atmos. Environ. 43, 6271–6278 (2009). coronavirus. Build. Environ. 183, 107186 (2020). 100. O. Miron, K.-H. Yu, R. Wilf-Miron, I. Kohane, N. Davidovitch, COVID-19 infections fol- 72. B. Blocken et al., Can indoor sports centers be allowed to re-open during the COVID- lowing physical school reopening. Arch. Dis. Child., 10.1136/archdischild-2020-321018 19 pandemic based on a certificate of equivalence? Build. Environ. 180, 107022 (2020). (2020). 73. C.-C. Chen, K. Willeke, Aerosol penetration through surgical masks. Am. J. Infect. 101. J. Zhang et al., Changes in contact patterns shape the dynamics of the COVID-19 Control. 20, 177–184 (1992). outbreak in China. Science 368, 1481–1486 (2020). 74. T. Oberg, L. M. Brosseau, Surgical mask filter and fit performance. Am. J. Infect. 102. K. Khan, J. W. M. Bush, M. Z. Bazant, COVID-19 indoor safety guideline. https:// Control. 36, 276–282 (2008). indoor-covid-safety.herokuapp.com. Accessed 6 April 2021. 75. A. Konda et al., Response to letters to the editor on aerosol filtration efficiency of 103. S. J. Olsen et al., Transmission of the severe acute respiratory syndrome on aircraft. common fabrics used in respiratory cloth masks: Revised and expanded results. ACS N. Engl. J. Med. 349, 2146–2422 (2003). Nano 14, 10764–10770 (2020). 104. K.-S. Kwon et al., Evidence of long-distance droplet transmission of SARS-CoV-2 by 76. Y. Li et al., Transmission of communicable respiratory infections and facemasks. J. direct air flow in a restaurant in Korea. J. Kor. Med. Sci. 35, e415 (2020). Multidiscip. Healthc. 1, 17 (2008). 105. F. Ciriello, G. R. Hunt, Analytical solutions and virtual origin corrections for forced, 77. S. Asadi et al., Efficacy of masks and face coverings in controlling outward aerosol pure and lazy turbulent plumes based on a universal entrainment function. J. Fluid particle emission from expiratory activities. Sci. Rep. 10, 1–13 (2020). Mech. 893, A12 (2020). 78. J. Pan, C. Harb, W. Leng, L. C. Marr, Inward and outward effectiveness of cloth masks, 106. F. Yang, A. A. Pahlavan, S. Mendez, M. Abkarian, H. A. Stone, Towards improved social a surgical mask, and a face shield. Aerosol Sci. Technol., 10.1080/02786826.2021. distancing guidelines: Space and time dependence of virus transmission from speech- 1890687 (2021). driven aerosol transport between two individuals. Phys. Rev. Fluids 5, 122501(R) 79. L. Nicolaou, T. A. Zaki, Characterization of aerosol Stokes number in 90◦ bends and (2020). idealized extrathoracic airways. J. Aerosol Sci. 102, 105–127 (2016). 107. R. K. Bhagat, M. S. D. Wykes, S. B. Dalziel, P. F. Linden, Effects of ventilation on the 80. P. van den Driessche, Reproduction numbers of infectious disease models. Infect. Dis. indoor spread of COVID-19. J. Fluid Mech. 903, F1 (2020). Model. 2, 288–303 (2017). 108. M. Z. Bazant, et al., Monitoring carbon dioxide to quantify the risk of indoor air- 81. Y. Liu, A. A. Gayle, A. Wilder-Smith, J. Rocklov,¨ The reproductive number of COVID-19 borne transmission of COVID-19. medRxiv [Preprint] (2021). https://doi.org/10.1101/ is higher compared to SARS coronavirus. J. Trav. Med. 27, 1–4 (2020). 2021.04.04.21254903 (Accessed 9 April 2021).

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