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(a) A visual representation of the various terms used in part (a), illustrating their physical origin. (b) Equation describing how an estimate for the threshold dose for infection, N0, can be inferred from case data. The equation naturally divides into several components, one originating from medical data on virion emission rates for index patients, another that amounts to an effective room volume and incorporates environmental factors, a term that accounts for the volume inhaled by the patient, and one from epidemiological data on the attack rate.
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Fig 1 illustrates the model principle and key parameters: an index patient releases a volume of aerosols per unit time at , and each aerosol contains rho virions/unit volume.
Flow chart illustrating the main conceptual thread of the paper, originating with raw data (either measured or inferred) from a series of case studies.. The attack rate r from these data then fed into an infection-rate model (purple lines) which is used to estimate the inhaled quanta q for each case. A box airborne transmission model (green lines) is then used to calculate , the time-averaged rate of quanta emission from the index patient across the event. The mean of these values across cases is used to estimate  (for each activity). We can use this estimate (1) to predict , the attack rate of a hypothetical future event, and (2) to infer  by using literature values for infective load rho and viral emission rate  combined with the estimated  above.
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Fig 2 shows how each case's physical or epidemiological parameters (V, G, B, T, r) give a value of  for that case, which are averaged across cases to give an estimate of the emission rate  used to estimate the infection rate  in a hypothetical scenario.
Attack rate r (infected / exposed) and quanta inhaled q = -ln(1 - r) for each of the five events.. In the case of the choir, the smaller attack rate includes only confirmed cases, while the larger attack rate includes both confirmed and probable cases. In the cases of the Hunan buses, the range spans the two bus rides.
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Each of the five cases provides an infection rate (also called attack rate) r equal to the fraction of exposed individuals who were infected. r can be used to then estimate q in each case (Fig 3).
Key inputs and outputs.. (a) Diamonds show the interaction time T and room volume V for each of the five cases, presented in the same order for both panels. Event 1 = Skagit choir, 2 = Korean call center, 3 = Korean fitness center, 4 = Buddhist bus, 5 = Hunan buses. (b) Estimated quanta emission rates for each case: Sq (event specific, top panel), Sq,talking (middle panel), Sq,breathing (bottom panel). Because each event has a different mix of activities (time spent singing/talking versus breathing), the estimated event quanta emission rate Sq ranges over 2 orders of magnitude. However, the estimated quanta emission rates for talking and breathing alone (Sq,talking) range over only a factor of ~6, which is also narrower than the range in T and V. (c) Values of viral load rho and aerosolized volume phi used in this work (triangles) and in literature (circles). rho: (1) value used in this work (107 copies/mL); (2) modeled peak viral load found by Goyal et al. across 25 patients; (3) range observed by Kleiboeker et al. across 4,432 patients; phi: Breathing (4) value used in this work (6.0 x 10-4 mL/hr); (5) range implied from Miller et al. based on Morawska et al.; (6) range implied from Stadnytskyi et al. (using ratio of breathing/speaking in Morawska) et al.; (7) range based on exhaled breath condensate (EBC) dilution measurements; Talking (8) value used in this work (2.7 x 10-2 mL/hr); (9) range in Miller et al. and Morawska et al. (1-10 nL/hr); (10) range in Stadnytskyi et al.; (11) range in Smith et al.; (d) Estimated characteristic infective dose N0 for each of the five cases.
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In each case, the observed  results from different activities (e.g. singing in the choir case, versus largely breathing in the bus ride cases); we use relationships between relative expulsion rates in different activities from the literature to standardize the quanta emission rates for breathing  or talking alone  (Fig 4).
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