key: cord-1013843-ynk1f41i authors: Haas, Charles N. title: Action Levels for SARS‐CoV‐2 in Air: Preliminary Approach date: 2021-04-05 journal: Risk Anal DOI: 10.1111/risa.13728 sha: 639797885f4337580d335b7eb4cb9d99788a005d doc_id: 1013843 cord_uid: ynk1f41i Quantitative microbial risk assessment has been used to develop criteria for exposure to many microorganisms. In this article, the dose–response curve for Coronavirus 229E is used to develop preliminary risk‐based exposure criteria for SARS‐CoV‐2 via the respiratory portals of entry. Modeling studies also indicate that both routes are important in the health care setting (Jones, 2020) . For both of the above mechanisms, the portal of entry is the respiratory system. However, the size of the particle will influence its deposition within the respiratory tract (Haddrell et al., 2015) . There is also a potential portal of entry via shortrange deposition to the eye (Chu et al., 2020; Mac-Intyre & Wang, 2020) . However, this portal of entry will not be considered in this article. A critical task for determination of control strategies is to determine doses that would be regarded as acceptable. Then the corresponding environmental (e.g., air) concentrations can be computed. By comparing these to the air concentrations resulting from uncontrolled settings in the presence of sources (one of more infected individuals emitting virus), one can then determine the magnitude of source reduction needed. This can be implemented in a variety of ways, including a layered, or multiple barrier, approach consisting of use of masks, ventilation, and active air treatment systems. The objective of this article is to provide a preliminary framework to the determination of acceptable air levels of virus using a quantitative microbial risk assessment (QMRA) approach (Haas et al., 2014) . In this approach, once a hazard is identified, dose-response assessment and exposure assessment are performed, and combined in a risk characterization to estimate the risk and its uncertainty. In this application, a "reverse QMRA" is used in the sense of Soller et al. (2010) , wherein the dose corresponding to a particular acceptable risk is calculated. Watanabe et al. (2010) reviewed the literature for available data sets (human and animal) for development of dose-response models for various coronaviruses. Of these, there was only one human data set (with Coronavirus 229E) and this had the lowest median effective dose (most potent). This will be used in this analysis. The underlying data were from experimental work by Bradburne et al. (1967) in which human volunteers were dosed into their nostrils with different amounts of virus. The endpoint response was illness. Watanabe et al. (2010) found that the exponential dose-response model (Equation (1)) provided good fit to the data. In this equation, d is the average dose (in this case, plaque forming units-pfu-of virus), k is the dose-response parameter (interpreted as the inverse of the probability that one virus will survive and initiate the endpoint effect), and p is the risk. There are multiple, equivalent, ways of interpreting p. It can be regarded as the probability that a single individual exposed to the average dose of d will have the effect. It can also be interpreted as the expected proportion of individuals exposed to the average dose of d who will have the adverse effect. Finally (and in the interpretation used below), it can be regarded as the number of individuals who would need to be exposed to the average dose such that one adverse case would be expected. The fit to the dose-response data will be used to ascertain the number of individuals exposed to a particular average dose that would be required to observe at least one adverse case. To translate dose to concentration in the air, which is being inhaled, a breathing rate and a duration of exposure is needed. In the example below, a light intensity breathing rate of 0.012 m 3 /min was used (https://www.epa.gov/sites/production/files/ 2015-09/documents/efh-chapter06.pdf). Different scenarios and intensities of breathing would require use of a different breathing rate. The (Watanabe et al., 2010) fit to the data of Bradburne et al. (1967) is shown in Fig. 1 . The best fit value of k is 18.54, indicating that each pfu has a probability of 0.054 of causing an adverse effect. By taking the reciprocal of "p" in Equation (1), we can calculate the number of persons who would be required to be exposed to an average dose in order to expect to observe one case. This analysis is shown in Fig. 2 . Note that this is a straight line with a slope of unity on a log-log plot since at low doses, the exponential dose-response relationship is closely approximated by a linear relationship. As an example of the use of Fig. 2 , if 100 people are of interest, then an average exposed dose of less than 0.18 pfu would be needed to be below the critical line. This could be translated into an air concentration if a breathing rate and duration were stipulated. As an example, if the time of exposure was one hour, and with the breathing rate given above, the dose corresponds to a virus concentration of 0.25 pfu/m 3 . Note that in this example, results are given in terms of pfu-that is, viable and infectious virus. In much environmental surveillance, including of SARS-CoV-2, measurements are taken of nucleic acid (RNA) in units of gene copies (gc). There is considerable difference between these measurements, which may reflect differences between viability and total measurable viral components and experimental limitations (Haas, 2020) . This ratio has yet to be measured for SARS-CoV-2. For the influenza viruses, also enveloped RNA viruses, in clinical samples, the ratio has been reported as between 185 and 708 gc/pfu (Ip et al., 2015) . It is expected that with environmental holding, this ratio would increase with the greater decay of viability compared to nucleic acid fragments. An alternative or complementary approach to viewing the data is to look at the probability of having one or more cases given an average dose and population size. If p is the probability of an individual subject having the adverse affect, and if N individuals are subject to that risk, then by binomial statistics the probability of one or more adverse effects is given by In Equation (2), "p" can be replaced by the dose-response relationship from Equation (1) to yield (3) Probability of one or more cases as a function of average exposure and number exposed. Finally, rearranging Equation (3) we obtain For various values of exposed population size and probability, Equation (4) is shown in Fig. 3 . So, for example, if 100 people are exposed and it is desired to keep the risk of a case below 1%, then the maximum average dose must be below 0.0011 pfu. With an assumed exposure duration and breathing rate, this can be translated into an average air concentration as per the previous example. This analysis uses 229E as the coronavirus for reference. This is an alphacoronavirus, in contrast to SARS-CoV-2, which is a betacoronavirus (Liu et al., 2021) . Whether the betacoronaviruses have substantially different dose-response behavior remains to be seen, and would likely require testing in suitable animal models. The other viruses analyzed by Watanabe et al. (2010) show lesser potency than 229E. This report develops relationships based on viable infectious virus (pfu). Most environmental studies have performed measurements based on gc of viral RNA isolated. The relationship between the two, and the effect of holding conditions on this relationship are not known. A study in a hospital in Nebraska observed up to 50 gc/L in air samples in COVID19 patient areas (Santarpia et al., 2020) . Some of the environmental samples showed cypopathogenic effects (CPE) in tissue culture, although confirmation of SARS-CoV-2 could not be attempted. Lednicky et al. (2020) found 0.9 gc/L of SARS-CoV-2 in air samples in a student clinic. When cultured, CPE was observed, although confirmation of the virus in the tissue culture was not performed. In hospitalized patients, it was observed that swab samples were not positive for a viable virus until polymerase chain reaction (PCR) titers were in excess of 10 6 RNA copies (van Kampen et al., 2020) . It is known, however, that virus can be produced in substantial numbers in presymptomatic cases, perhaps at even greater amounts than in symptomatic and hospitalized cases (Arons et al., 2020) . Therefore a "typical" value for a ratio between viable infectious virus and gc in environmental samples remains unclear. The underlying dose-response study used in this development was based on direct placement of drops in the nostrils. The impact and potential differences associated with inhalation of smaller particles, which may have a greater chance of deeper penetration into the respiratory tract, remain uncertain. If an acceptable level of risk were stipulated, then as shown above, levels of air concentrations that correspond to that risk in different scenarios could be attained. Ascertainment of acceptable risk requires social deliberation considering economics and equity (Fischhoff, 1994) . Among the considerations include the potential for social amplification of risk (Renn et al., 1992) . Detailed discussion is beyond the scope of this article. Using the dose-response relationship with specific assumptions of breathing rate and duration of exposure, this can be translated into air concentration. With this, estimation of source strength, and standard mass balance models of indoor air quality (Nazaroff, 2014) , the specification of needed interventions to control risk from air exposure can be undertaken. Clearly there are data gaps, and as new information emerges, the refinement of this approach can occur. However, in the design of interventions, it is important not to let the perfect be the enemy of the good, and it is becoming clear that we have quantitative tools to assist in the design of engineering interventions. 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