key: cord-0869660-2ez9vnrt
authors: Chen, P. Z.; Bobrovitz, N.; Premji, Z.; Koopmans, M.; Fisman, D. N.; Gu, F. X.
title: Heterogeneity in transmissibility and shedding SARS-CoV-2 via droplets and aerosols
date: 2020-10-15
journal: nan
DOI: 10.1101/2020.10.13.20212233
sha: 6265819045749bcfff84234ef016c996a4c1838e
doc_id: 869660
cord_uid: 2ez9vnrt

A growing number of studies provide insight into how SARS-CoV-2 spreads1-7. Yet, many factors that characterize its transmissibility remain unclear, including mechanistic correlates of overdispersion, viral kinetics, the extent to which respiratory droplets and aerosols carry viable virus and the infectiousness of asymptomatic, presymptomatic and pediatric cases7. Here, we developed a comprehensive dataset of respiratory viral loads (rVLs) via systematic review and investigated these factors using meta-analyses and modeling. By comparing cases of COVID-19, SARS and influenza A(H1N1)pdm09, we found that heterogeneity in rVL was associated with overdispersion and facilitated the distinctions in individual variation in infectiousness among these emergent diseases. For COVID-19, case heterogeneity was broad throughout the infectious period, although rVL tended to peak at 1 day from symptom onset (DFSO) and be elevated for 1-5 DFSO. While most cases presented minimal risk, highly infectious ones could spread SARS-CoV-2 by talking, singing or breathing, which shed virions at comparable rates via droplets and aerosols. Coughing shed considerable quantities of virions, predominantly via droplets, and greatly increased the contagiousness of many symptomatic cases relative to asymptomatic ones. Asymptomatic and symptomatic infections showed similar likelihoods of expelling aerosols with SARS-CoV-2, as did adult and pediatric cases. Children tended to be less contagious by droplet spread than adults based on tendencies of symptomatology rather than rVL. Our findings address longstanding questions on SARS-CoV-2 transmissibility and present pertinent considerations for disease control.

factors that characterize its transmissibility remain unclear, including mechanistic correlates of 23 overdispersion, viral kinetics, the extent to which respiratory droplets and aerosols carry viable 24 virus and the infectiousness of asymptomatic, presymptomatic and pediatric cases 7 . Here, we 25 developed a comprehensive dataset of respiratory viral loads (rVLs) via systematic review and 26 investigated these factors using meta-analyses and modeling. By comparing cases of COVID-19, 27 SARS and influenza A(H1N1)pdm09, we found that heterogeneity in rVL was associated with 28 overdispersion and facilitated the distinctions in individual variation in infectiousness among 29 these emergent diseases. For COVID-19, case heterogeneity was broad throughout the infectious 30 period, although rVL tended to peak at 1 day from symptom onset (DFSO) and be elevated for 1-31 5 DFSO. While most cases presented minimal risk, highly infectious ones could spread SARS-32

CoV-2 by talking, singing or breathing, which shed virions at comparable rates via droplets and 33 aerosols. Coughing shed considerable quantities of virions, predominantly via droplets, and 34 greatly increased the contagiousness of many symptomatic cases relative to asymptomatic ones. 35

Asymptomatic and symptomatic infections showed similar likelihoods of expelling aerosols with 36 SARS-CoV-2, as did adult and pediatric cases. Children tended to be less contagious by droplet 37 spread than adults based on tendencies of symptomatology rather than rVL. Our findings address 38 coincides with atomization, we used Poisson statistics to model likelihood profiles. To calculate 135 an unbiased estimator of partitioning (the expected number of viable copies per particle), our 136 method multiplied rVL estimates with the volumes of atomized particles and an assumed 137 viability proportion of 0.1% after dehydration (Methods). 138

When expelled by the mean COVID-19 case across the infectious period, respiratory 139 particles showed minimal likelihoods of carrying viable SARS-CoV-2 ( Fig. 4a,b) . Aerosols 140 (dehydrated aerodynamic diameter [da]≤5 µm) were <0.001% likely to contain a virion. Droplets 141 also had low likelihoods: at da=40 µm, they were ≤0.4% likely to contain a virion. 142 COVID-19 cases with high rVLs, however, expelled particles with considerably greater 143 likelihoods of carrying viable copies (Fig. 4a,b) . For the 98 th cp at 1 DFSO, 18.2% (8.8-27.6%) 144 of aerosols (da=5 µm) contained at least one SARS-CoV-2 virion. For da>14.4 µm, droplets were 145 >99% likely to contain virions, with large ones carrying tens to hundreds. 146 aerosols and droplets: aerosols mediated 25.2-43.4% of the virions expelled by the non-156 presenting activities (Fig. 4g) . In comparison, coughing shed far greater quantities of virions 157 ( Fig. 4f) , of which >99.9% were carried by droplets. 158 We further examined the influences of case heterogeneity and disease course on expelling 159 SARS-CoV-2 (Fig. 4h, Extended Data Fig. 5 ). The estimated total shedding rates (over all 160 particle sizes) for a respiratory activity spanned ≥8.55 orders of magnitude on each DFSO; 161 cumulatively from -1 to 10 DFSO, they spanned 11.2 orders of magnitude. Hence, most cases 162 Fig. 5c ). At -1 and 10 DFSO, these estimates were reduced by ~2 orders of 172 magnitude. Thus, most symptomatic cases shed considerable quantities of SARS-CoV-2 by 173 coughing; a single cough accounted for the virions emitted by weeks of singing for a case. 174 tends to be greatest soon after illness rather than in the presymptomatic period, which concurs 202 with large tracing studies (6.4-12.6% of secondary infections from presymptomatic 203 transmission) 26,27 rather than early temporal models (~44%) 14 . Furthermore, our kinetic analysis 204 suggests that, on average, SARS-CoV-2 reaches diagnostic concentrations 1.60-3.22 days after 205 respiratory infection (-3.78 to -2.16 DFSO), assuming assay detection limits of 1-3 log10 206 copies/ml, respectively, for nasopharyngeal swabs immersed in 1 ml of transport media. 207

Third, we modeled the likelihood of shedding SARS-CoV-2 via aerosols. Talking, singing 208 and breathing shed SARS-CoV-2 at comparable rates through droplets and aerosols (up to tens to 209 hundreds of virions/min). As airborne spread is recognized as a key mode of transmission for 210 A(H1N1)pdm09 20 , our model estimates and comparative analyses support, particularly for highly 211 infectious cases, airborne spread as a transmission mode for SARS-CoV-2. While our models 212 delineated aerosols from droplets at the classical threshold (da=5 µm), recent reports show that, 213 based on emission vectors and environmental conditions, respiratory particles larger than 5 µm 214

can also travel >2 m in air 28,29 , further supporting the plausibility of the airborne transmission of 215 SARS-CoV-2. However, with short durations of stay in well-ventilated areas, the concentration, 216 and exposure risk, of aerosols remains correlated with proximity to infectious cases 18,28 . 217 Fourth, we assessed the relative infectiousness of COVID-19 subgroups. Since rVL 218 distributions are similar among subgroups and the predominant source of aerosols is the non-219 presenting respiratory activities (talking, singing and breathing), symptomatic and asymptomatic 220 infections present similar risks for aerosol spread, as do adult and pediatric cases. However, most 221 cases shed considerable numbers of virions via large droplets by coughing, a common symptom 222 of COVID-19 30 . Thus, symptomatic infections tend to be significantly more contagious than 223 asymptomatic ones, providing a reason as to why asymptomatic cases transmit SARS-CoV-2 at 224 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint lower relative rates 3 , especially in close contact 31 , despite similar rVLs and increased contact 225 patterns. Accordingly, children (48-54% of symptomatic cases present with cough) 32,33 tend to be 226 less contagious by droplet spread than adults (68-80%) 30,33 based on tendencies of 227 symptomatology rather than rVL. 228

Our study has limitations. The systematic search found a limited number of studies reporting 229 quantitative specimen measurements from the presymptomatic period, meaning these estimates 230 may be sensitive to sampling bias. Although additional studies have reported semiquantitative 231 metrics (cycle thresholds), these data were excluded because they cannot be compared on an 232 absolute scale due to batch effects 34 , limiting use in compound analyses. Furthermore, our 233 analyses considered population-level estimates of the infectious periods and viability 234

proportions, which omit individual variation in the dynamics of virus viability. Some patients 235

shed SARS-CoV-2 with diminishing viability soon after symptom onset 13 , while others produce 236 replication-competent virus for weeks 35 . It remains unelucidated how case characteristics and 237 environmental factors affect the viability dynamics of SARS-CoV-2. 238

Taken together, our findings provide a potential path forward for disease control. They 239 highlight the disproportionate role of high-risk cases, settings and circumstances in propelling 240 the COVID-19 pandemic. Since highly infectious cases, regardless of age or symptomatology, 241 can rapidly shed SARS-CoV-2 via both droplets and aerosols, airborne spread should also be 242 recognized as a transmission risk, including for superspreading. Strategies to abate infection 243 should limit crowd numbers and duration of stay while reinforcing distancing and then 244 widespread mask usage; well-ventilated settings can be recognized as lower risk venues. 245

Coughing sheds considerable quantities of virions for most infections, while rVL tends to peak at 246 1 DFSO and can be high throughout the infectious period. Thus, immediate, sustained self-247 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint isolation upon symptom presentation is crucial to curb transmission from symptomatic cases. 248

While diagnosing COVID-19, qRT-PCR can also help to triage contact tracing, prioritizing 249 patients with higher specimen measurements: for nasopharyngeal swabs immersed in 1 ml of 250 transport media, ≥7.14 (7.07-7.22, 95% CI) log10 copies/ml corresponds to ≥80 th cp. Doing so 251 may identify asymptomatic and presymptomatic cases more efficiently, a key step towards 252 mitigation as the pandemic continues. 253 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

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The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint their size relationship with dehydrated aerodynamic diameter (da), but not likelihood of 377 containing virions during atomization. For higher no. of virions, some likelihood curves were 378 omitted to aid visualization. When the likelihood for 0 virions approaches 0%, particles are 379 expected to contain at least one viable copy. c-f, Rate that the mean and 98 th -cp COVID-19 cases 380 at 1 DFSO shed viable SARS-CoV-2 by talking (c), singing (d), breathing (e) or coughing (f) 381 over da. g, Relative contribution of aerosols (da≤5 μm, red bar) and droplets (da>5 μm, blue bar) 382 to shedding virions for the respiratory activities. h, Case heterogeneity in the total shedding rate 383 (over all particle sizes) of virions via singing across the infectious period. Earlier 384 presymptomatic days were excluded based on limited data. Data range between the 1 st and 99 th 385 cps. Lines and bands represent estimates and 95% CIs, respectively, for likelihoods or Poisson 386 means. 387 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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We undertook a systematic review and prospectively submitted the systematic review protocol 390 for registration on PROSPERO (registration number, CRD42020204637). Other than the title of 391 this study, we have followed PRISMA reporting guidelines 36 . The systematic review was 392 conducted according to Cochrane methods guidance 37 . 393

The search included papers that (i) reported positive, quantitative measurements (copies/ml 394 or an equivalent metric) of SARS-CoV-2, SARS-CoV-1 or A(H1N1)pdm09 in human 395 respiratory specimens (ETA, NPA, NPS, OPS, POS and Spu) from COVID-19, SARS or 396 A(H1N1)pdm09 cases; (ii) reported data that could be extracted from the infectious periods of 397 SARS-CoV-2 (defined as -3 to +10 DFSO for symptomatic cases and 0 to +10 days from the day 398 of laboratory diagnosis for asymptomatic cases), SARS-CoV-1 (defined as 0 to +20 DFSO or the 399 equivalent asymptomatic period) or A(H1N1)pdm09 (defined as -2 to +9 DFSO for symptomatic 400 cases and 0 days to +9 days from the day of laboratory diagnosis for asymptomatic cases); and 401 (iii) reported data for two or more cases with laboratory-confirmed COVID-19, SARS or 402 A(H1N1)pdm09. Quantitative specimen measurements were considered after RNA extraction for 403 diagnostic sequences of SARS-CoV-2 (Ofr1b, N, RdRp and E genes), SARS-CoV-1 (Ofr1b, N 404 and RdRp genes) and A(H1N1)pdm09 (HA and M genes). 405

Studies were excluded, in the following order, if they (i) studied an ineligible disease; (ii) 406 had an ineligible study design, including those that were reviews of evidence (e.g., scoping, 407 systematic, narrative), did not include primary clinical human data, reported data for less than 408 two cases due to an increased risk of selection bias, were incomplete (e.g., ongoing clinical 409 trials), did not report an RNA extraction step before measurement or were studies measuring 410 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint environmental samples; (iii) reported an ineligible metric for specimen concentration (e.g., 411 qualitative RT-PCR or cycle threshold [Ct] values without calibration included in the study); (iv) 412 reported quantitative measurements from an ineligible specimen type (e.g., blood specimens, 413 pooled specimens or self-collected POS or Spu patient specimens in the absence of a healthcare 414 professional); (v) reported an ineligible sampling period (consisted entirely of data that could not 415 be extracted from within the infectious period); or (vi) were duplicates of an included study (e.g., 416

preprinted version of published paper or duplicates not identified by Covidence). We included 417 data from control groups receiving standard of care in interventional studies but excluded data 418 from the intervention group. Patients in the intervention group are, by definition, systematically 419 different from general case populations because they receive therapies not being widely used for 420 treatment, which may influence virus concentrations. Interventional studies examining the 421 comparative effectiveness of two or more treatments were excluded for the same reason. Studies 422 exclusively reporting semiquantitative measurements (e.g., Ct values) of specimen concentration 423 were excluded, as these measurements are sensitive to batch inconsistencies and, without proper 424 calibration, cannot be compared on an absolute scale across studies 34 . 425

We searched, without the use of filters or language restrictions, the following sources: 426 and Emerging Sources Citation Index, 2015 to 7 August 2020), as well as MedRxiv and BioRxiv 433 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. prevalence studies 38-40 . To evaluate the sample size in a study, we used the following calculation: 449

where ! * is the sample size threshold, # is the z-score for the level of confidence (95%), $ is the 451 standard deviation (assumed to be 3 log10 copies/ml, one quarter of the full range of rVLs) and % 452 is the marginal error (assumed to be 1 log10 copies/ml, based on the minimum detection limit for 453

qRT-PCR across studies) 41 . The hybrid JBI critical appraisal checklist is shown in the 454 Supplementary Notes. Inconsistencies were resolved by discussion and consensus. 455 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. graphically. For included studies, we also collected the relevant numbers of cases, types of cases, 459 volumes of transport media, pharmacotherapies, DFSO (for symptomatic cases) or day relative to 460 initial laboratory diagnosis (for asymptomatic cases) on which each specimen was taken and 461 numbers of tested specimens. Hospitalized cases were defined as those being tested in a hospital 462 setting and then admitted. Non-admitted cases were defined as those being testing in a hospital 463 setting but not admitted. Community cases were defined as those being tested in a community 464 setting. Symptomatic, presymptomatic and asymptomatic infections were defined as in the study. 465

Based on rare description in the included studies, paucisymptomatic infections, when defined in 466 a study, were included with symptomatic ones. Pediatric cases were defined as those of 18 years 467 of age or lower or as defined in the study. Adult cases were defined as those above 18 years of 468 age or as defined in the study. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint expected uptake volume for swabs (0.128 ± 0.031 ml, mean ± SD) 103 or reported collection 480 volume for expulsed fluid in each study (e.g., 0.5 to 1 ml) along with the reported volume of 481 transport media in each study (e.g., 1 ml), we calculated the dilution factor for each respiratory 482 specimen to estimate the rVLs. If the diluent volume was not reported, then the dilution factor 483 was calculated assuming a volume of 1 ml (NPS and OPS), 2 ml (POS and ETA) or 3 ml (NPA) 484 of transport media 43,45,71 . Unless dilution was reported for Spu specimens, we used the specimen 485 measurement as the rVL 13 . The non-reporting of diluent volume was noted as an element 486 increasing risk of bias in the hybrid JBI critical appraisal checklist. Viral load estimates (based 487 on instrumentation, calibration, procedures and reagents) are not standardized. While the above 488 procedures (including only quantitative measurements after extraction, collecting assay detection 489 limits, correcting for specimen dilution) have considered many of these factors, non-490 standardization is an inherent limitation in interpreting specimen measurements across studies. 491

Pooled estimates and 95% CIs for the expected rVL of each virus across their infectious 492 period were calculated using a random-effects meta-analysis. The estimates for rVL assumed 493 that each viral copy was extracted and quantified from the tested specimen aliquot. For studies 494 reporting summary statistics in medians and interquartile or total ranges, we derived estimates of 495 the mean and variance and calculated the 95% CIs 104 . All calculations were performed in units of 496 log10 copies/ml. Between-study heterogeneity in meta-analysis was assessed using the I 2 and τ 2 497 statistics. The weighting for each study in its virus group was calculated as the reciprocal of the 498 rVL variance. 499 500

. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint Subgroup analyses were conducted to compare the expected rVLs of SARS-CoV-2 in adult, 502 pediatric, symptomatic and asymptomatic COVID-19 cases, as previously defined, during the 503 infectious period. The overall estimate for each subgroup was the expected rVL when 504 encountering a case of that subgroup during the infectious period. Studies reporting data 505 exclusively from a subgroup of interest were included in the analysis without modification. For 506 studies in which data for these subgroups constituted only part of its dataset, rVLs from the 507 subgroup were collected to calculate the mean, variance and 95% CIs. All calculations were 508 performed in units of log10 copies/ml. In the analysis, we excluded studies with only a single case 509 in our subgroups of interest. Pooled estimates and 95% CIs for each subgroup were calculated 510 using a random-effects meta-analysis, in which between-study heterogeneity was assessed using 511 the I 2 and τ 2 statistics. The weighting for each study in its subgroup was calculated as the 512 reciprocal of the rVL variance. 513 514

To analyze heterogeneity in rVLs, we pooled the entirety of individual sample data (reported as 516 individual specimen measurements rather through descriptive statistics) in the systematic dataset 517 by disease, COVID-19 subgroups and DFSO. For analyses of SARS-CoV-2 dynamics across 518 DFSO, we included estimated rVLs from negative qRT-PCR measurements of respiratory 519 specimens (n=3, 3, 6, 8, 12, 15, 13, 17 and 14 negative specimens for 2, 3, 4, 5, 6, 7, 8, 9 and 10 520 DFSO, respectively) for cases that had previously been quantitatively confirmed to have 521 COVID-19. These rVLs were estimated based on the reported assay detection limit in the 522 respective study. Probability plots and modified Kolmogorov-Smirnov tests were used to 523 determine the suitability of normal, lognormal, gamma and Weibull distributions to describe the 524 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint distribution of rVLs for SARS-CoV-2, SARS-CoV-1 and A(H1N1)pdm09. For each virus, the 525 data best conformed to Weibull distributions, which is described by the probability density 526 function 527

where , is the shape factor, -is the scale factor and + is rVL (+ ≥ 0 log10 copies/ml). In this 529 distribution, the value of the rVL at the 4 th percentile was determined using the quantile function, 530

(3) 531

For cp curves, we used eq. (3) to determine rVLs from the 1 st cp to the 99 th cp (step size, 1%). 532

Curve fitting to eq. (2) and calculation of eq. (3) and its 95% CI was performed using the 533 Distribution Fitter application in Matlab R2019b (MathWorks, Inc., Natick, Massachusetts, 534 USA). 535 536

To assess the relationship between k and heterogeneity in rVL, we performed a univariate meta-538 regression (log > = ?(@A) + C, where ? is the slope for association and C is the intercept) 539 between pooled estimates of k (based on studies describing community transmission) for 540 COVID-19 (k=0.409) 4-6,105-108 , SARS (k=0.165) 17 and A(H1N1)pdm09 (k=8.155) 22,23 and the SD 541 of the rVLs in each study. Since the negative binomial distribution, from which k is derived 17 , is 542 analogous to a compound Poisson distribution in which each random variable is Log(>)-543 distributed, the meta-regression was performed with log >. Based on negligible between-study 544 heterogeneity, we used a fixed-effects model. This analysis assumes that the SD of rVLs in each 545 study estimates SD of rVL for the disease. Thus, for weighting in the meta-regression, we used 546 the proportion of rVL samples for each study relative to the entire systematic dataset (E , = 547 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint presented along with the p-value for association (meta-regression slope t-test for ?) between the 549 two variables. The meta-regression assumed that the viability proportion (for viruses exiting the 550 respiratory tract) was similar across cases for a given respiratory infection; it could be a different 551 value for different diseases. The meta-regression also assumed that the rate profile of particles 552 expelled by respiratory activities (e.g., talking) is similar among the diseases. Massachusetts, USA) via the Runge-Kutta method and initial parameters I 1 , K 1 and G 1 of 4 582 copies/ml, 0 cells and 5×10 7 cells, respectively, for the range -5 to 10 DFSO. The analysis was 583 first performed with eqs. (8)-(9). These output parameters were then used to initialize final 584 analysis using eqs. (4)-(6), where the estimates forand L were input as fixed and variable 585 parameters, respectively. The fitted line and its coefficient of determination (r 2 ) were presented. 586

To estimate the average incubation period, we extrapolated the kinetic model to 0 and 1 587 log10 copies/ml pre-symptom onset. To estimate the average duration of shedding, we 588 extrapolated the model to 0 log10 copies/ml post-symptom onset. Unlike experimental estimates, 589 this estimate for duration of shedding was not defined by assay detection limits. These analyses 590 had limitations. To estimate the average DFSO on which SARS-CoV-2 concentration reached 591 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint diagnostic levels, we extrapolated the model pre-symptom onset to the equivalent of 1 and 3 592 log10 copies/ml in specimen concentration (chosen as example assay detection limits), as 593 described by the dilution factor estimation above. The average time from respiratory infection to 594 reach diagnostic levels was then calculated by subtracting these values from the incubation 595 period for 0 log10 copies/ml. However, the extrapolated time for SARS-CoV-2 to reach 596 diagnostic concentrations in the respiratory tract should be validated in tracing studies, in which 597 contacts are prospectively subjected to daily sampling. 598 599

The desiccation time of a particle in air was described H 456 = C $% (% 7 " − % 456 " ), where C is 601 prefactor for dehydration rate which depends on the environmental conditions, % 7 is the initial 602 hydrated diameter and % 456 is particle diameter after desiccation 111 . After desiccation, the 603 remaining non-volatile matter (ions, molecules, viruses and cells) governs particle size, which is 604 approximately 0.44 times the initial size of particles atomized in the respiratory tract 112 . 605

Dehydrated aerodynamic diameter was calculated by % 9 = % : (V/V 1 ) %/" , where % : is the 606 dehydrated particle size, V is the material density of the respiratory particle and V 1 is the 607 reference material density (1 g/cm 3 ). For conservative estimates, the value of b was taken to be 608 64.9 µm 2 /s 113 based on conditions of room temperature and a relative humidity of 59% (near the 609 upper limit of 60% for healthcare and typical indoor specifications) 114 . The equation for 610 desiccation time indicated that respiratory particles begin to dehydrate immediately upon release 611 to the ambient environment. Desiccation occurred rapidly, as the equation estimated that an 11.4-612 µm particle desiccated to 5 µm in 1.6 s within the model conditions, and this value was an upper 613 limit for the desiccation times of aerosols (H 456 ≤ 1.6 s). 614 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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To calculate an unbiased estimator for viral partitioning (the expected number of viable copies in 617 an expelled particle at a given size), we multiplied rVLs with the volume equation for spherical 618 particles during atomization and the estimated viability proportion: 619

where X is the expectation value, V is the material density of the respiratory particle (997 g/m 3 ), 621 Z : is the volumetric conversion factor (1 ml/g), [ is the viability proportion, + is the rVL and % is 622 the hydrated diameter of the particle during atomization. The model assumed [ was 0.1% for the 623 viruses. For influenza, approximately 0.1% of copies in particles expelled from the respiratory 624 tract represent viable virus 115 , which is equivalent to one in 3 log10 copies/ml for rVL or, after 625 dilution in transport media, roughly one in 4 log10 copies/ml for specimen concentration. Recent 626 reports have detected culture-positive respiratory specimens with SARS-CoV-2 concentrations 627 down to 4 log10 copies/ml 13 , including from pediatric patients 62 and in the presymptomatic 628 period 15 , suggesting the assumption was also suitable for SARS-CoV-2. 629

Likelihood profiles were determined using Poisson statistics, as described by the probability 630 mass function 631

where > is the number of virions partitioned within the particle. For X, 95% CIs were determined 633 using the variance of its rVL estimate. To determine 95% CIs for likelihood profiles from the 634 probability mass function, we used the delta method, which specifies 635

636 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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For the rate profiles of particles expelled during respiratory activities, we used distributions from 651 the literature. For coughing, we considered the rate (particles/cough) of expelling particles at 652 different sizes, as determined by Loudon and Roberts 118 , by calculating the mean number of 653 respiratory particles expelled per cough based on subject tests RI, RII, LI, LII and EI (EII was 654 presumed to be an outlier based on the relative rate when compared to EI). These particles were 655 taken to be dehydrated based on the deposition time in the experiment relative to estimated 656 dehydration rates. We compared this rate profile to that of Duguid 119 , which were taken to be 657 hydrated particles based on experimental design. For talking, singing and breathing, we obtained 658 data from Morawaska et al 120 . Rate profiles (particles/min) were calculated by converting the 659 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint normalized concentration (particles/cm 3 ) at each particle size based on normalization (32 660 channels per decade) for the aerodynamic particle sizer (APS) used, unit conversion (cm 3 to L) 661 and the sample flow rate (1 L/min). Rate profiles of talking and singing were isolated from 662 breathing by subtracting the contribution of breathing to the combined data. Particles were taken 663 to be dehydrated based on the minimum particle age in the measurements. Based on the APS 664 used, the analyzed range for da was 0.3-20 μm. While larger droplets may potentially be expelled 665 by the respiratory activities, the data suggested that their emission rates were minimal, and there 666 was a limited bias associated with instrumentation. We compared these data for talking with rate 667 profiles of talking loudly and talking quietly from Asadi et al 121 . For data reported in a size 668 channel, we took the particle size to be the median value. Curves based on discrete particle 669 measurements were connected using the nonparametric Akima spline function. 670 671

To determine the respiratory shedding rate across particle size, rVL estimates and the hydrated 673 diameters of particles expelled by a respiratory activity were input into eq. (10), and the output 674 was then multiplied by the rate profile of the activity (talking, singing, breathing or coughing). 675

Dehydration and viability considerations were continued from the likelihood models. The model 676 used particle profiles from (coughing) Loudon and Roberts 118 or (talking, singing and breathing) 677

Morawaska et al 120 . 678

To determine the total respiratory shedding rate for a given respiratory activity across cp, we 679 determined the cumulative hydrated volumetric rate (by summing the hydrated volumetric rates 680 across particle sizes for that respiratory activity) and input it into eq. (10). Using rVLs as 681 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint determined by the Weibull quantile functions, we then calculated the Poisson means and their 682 95% CIs at different cps. 683

To assess the relative contribution of aerosols and droplets to mediating respiratory viral 684 shedding for a given respiratory activity, we calculated the proportion of the cumulative hydrated 685 volumetric rate contributed by aerosols (da≤5 μm) or droplets (da>5 μm) for that respiratory 686 activity. Since the Poisson mean was proportional to cumulative volumetric rate, this estimate of 687 the relative contribution of aerosols and droplets to respiratory viral shedding was consistent 688 among viruses and cps in the model. 689

In this study, the model for shedding virions via droplets and aerosols did not delineate 690 particles generated in the upper respiratory tract from those generated in the lower respiratory 691 tract, as the sites of atomization remain poorly understood. It also did not differentiate cases with 692 significant expectoration from those without it. In addition, it did not account for individual Massachusetts, USA). Between-study heterogeneity in the random-effects meta-analyses was 701 assessed using the I 2 and τ 2 statistics. Probability plots for normal, lognormal, gamma and 702

Weibull distributions of rVLs were scored based on the Blom method. Modified Kolmogorov-703

Smirnov tests were used to determine the goodness of fits between rVLs (in log10 copies/ml) and 704 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint normal, lognormal, gamma or Weibull distributions. By accepting the null hypothesis in the 705 modified Kolmogorov-Smirnov test, the given distribution cannot be rejected to fit the data. 706

Based on fitted Weibull distribution parameters, the Weibull quantile function was used to 707 determine the rVL and its 95% CIs at a given cp. The association between k and rVL was 708 assessed via meta-regression, and the p-value for association was based on the meta-regression 709 slope t-test. Likelihood profiles were determined using the Poisson probability mass function and 710 the unbiased estimator for the expected partitioning of virions at a given particle size. sided Welch's t-test (relative to SARS-CoV-2), non-significance (p>0.05). 985

. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint with a logarithmic axis for diameter during atomization. 1021 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint coughing. a-c, Case heterogeneity in the total SARS-CoV-2 shedding rate (over all particle 1024 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint sizes) by talking at a moderate level (a), breathing (b) or coughing (c) for COVID-19 cases 1025 across the infectious period. Earlier presymptomatic days were excluded based on limited data. 1026 Data represent estimated rates for viable virus and range between the 1 st and 99 th cps. Lines and 1027 bands represent estimates and 95% CIs, respectively. 1028 . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint . CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted October 15, 2020. 

. CC-BY-NC 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted October 15, 2020. . https://doi.org/10.1101/2020.10.13.20212233 doi: medRxiv preprint

Comparison of SARS-CoV-2 detection in nasopharyngeal swab and 770 saliva

SARS-CoV-2 virus culture from the upper respiratory tract: 772 Correlation with viral load, subgenomic viral RNA and duration of illness

SARS-CoV-2 viral load in the upper respiratory tract of children and 775 adults with early acute COVID-19

Longitudinal analyses reveal immunological misfiring in severe COVID-777 19

Association of initial viral load in severe acute respiratory 779 syndrome coronavirus 2 (SARS-CoV-2) patients with outcome and symptoms

Hydroxychloroquine for early treatment of adults with mild Covid-19: a 782 randomized-controlled trial

Daily viral kinetics and innate and adaptive immune responses assessment 784 in COVID-19: a case series

Characteristics of pediatric SARS-CoV-2 infection and potential evidence for 787 persistent fecal viral shedding

SARS-CoV-2 in nasopharynx of symptomatic neonates, children, and adolescents

Viral RNA load in mildly symptomatic and asymptomatic children with

Viral load of SARS-CoV-2 in 799 clinical samples

Sequential analysis of viral load in a neonate and her mother infected with

Viral load dynamics in transmissible symptomatic patients with

Initial viral load and the outcomes of SARS

Early diagnosis of SARS coronavirus infection by real time RT-PCR

Nasopharyngeal shedding of severe acute respiratory syndrome-810 associated coronavirus is associated with genetic polymorphisms

Viral shedding in children infected by pandemic A/H1N1/2009 influenza 882 virus

Comparison of pandemic (H1N1) 2009 and seasonal influenza viral loads

Comparative epidemiology of pandemic and seasonal influenza A in 886 households

Viral load in patients infected with pandemic H1N1 2009 influenza A 888 virus

Influenza A(H1N1)pdm09 infection and viral load analysis in 890 patients with different clinical presentations

Performance of laboratory diagnostics for the detection of influenza

A(H1N1)v virus as correlated with the time after symptom onset and viral load

Clustering and superspreading potential of SARS-CoV-2 infections in

Pattern of early human-to-human transmission of Wuhan

Evaluating transmission heterogeneity and 916 super-spreading event of COVID-19 in a metropolis of China

Real-time monitoring the transmission potential of COVID-19 in

Extended Data Fig. 4. Rate profiles for particle expelled by respiratory activities. a,b, Rate 1015 profiles of particles expelled during coughing

Duguid 119 (b). c, Rate profile of particles expelled during singing, as obtained 1017 from Morawaska et al 120 . d,e, Rate profiles of particles expelled during talking. The data were SARS-CoV-1 (overall) §

These two columns summarize the cumulative number of specimens (left) collected from the number of studies (right) for each category in the systematic dataset

† The mean and sample SD were calculated on the entire set of individual sample data for each category

‡ The Weibull quantile distributions were used to determine rVLs at the 90 th , 95 th and 99 th cps

§ These categories included only rVL data from positive (above the detection limit) qRT-PCR measurements

|| Data for earlier DFSO were excluded from distribution fitting based on limited data, and empty cells were marked with

¶ These categories included negative qRT-PCR measurements (set at the detection limit to estimate rVLs

1041 ‡ For studies reporting specimen measurements as individual sample data (either in numerical or graphical formats), the sample data was extracted for analysis.1042 § Specimen measurements were converted to rVLs based on the dilution factor for specimens immersed in transport media.