BranchPattern’s Flu Infection Risk Estimator™ module is intended to estimate a) the aerosol influenza particle removal efficiency resulting from several different removal mechanisms and b) the associated probability of infection for adults and children, given a set of input conditions including space parameters, demographic factors, and time.
This module is one component of our Health and Productivity Performance Estimator (happē™) tool. The initial version of the tool was developed in 2009 to estimate the impact various indoor environmental quality (IEQ) conditions have on productivity and health. Based on IEQ peer reviewed research, it provides both percentage impacts and dollar amounts using weighted average salary dollars.
BranchPattern uses happē™ as part of pre- and post-occupancy evaluations to assess the impacts that existing space conditions are having on occupants. It’s also used during retrocomissioning and design to assess the relative impacts of different energy conservation measures (ECMs) or system types on productivity and health. BranchPattern has also found that making life cycle cost analyses more comprehensive increases the likelihood for sustainable and health/wellness focused decision-making throughout the design/construction process.
The module is set up to provide removal efficiencies and probabilities of Influenza infection for a baseline and design set of conditions. The “decrease in estimated number of flu infections via aerosol transmission,” the “decrease in salary dollars lost,” and the “decrease in child days lost” represent a subtraction of the design results from the baseline results. The module is not applicable to SARS-CoV-2 or other viruses. BranchPattern will continue evaluating if future versions of this tool could include modifications to account for SARS-CoV-2. However, that is dependent on the status of ongoing research.
The removal mechanisms addressed in this module include settling, ventilation (outdoor air), filtration (recirculation), and virus inactivation. A future update will include ultraviolet germicidal irradiation UVGI). The equations used to calculate the removal efficiencies are from Yang and Marr (2011), except for filtration. This was added based on the equations given in Stephens (2012).
If you’re using the tool to compare outputs from different ventilation, RH, or filtration inputs, selecting a removal time of 15 minutes, or 0.25 hours (the default value) seems to generally give the largest delta between the conditions being compared based on the underlying mathematical model. However, you can play with different removal times and evaluate the outcomes.
Two limitations inherent in the model presented by Yang and Marr (2011) are a) its basis on limited data obtained from laboratory experiments and b) the flu concentration calculations assume that droplets are instantaneously, continuously, and evenly distributed throughout the room. As with all models, this is a simplified version of what exists in reality.
Because a) interior temperatures do not range widely enough to significantly impact the results of the calculations and b) the dynamic viscosity of air doesn’t vary substantially with typical interior temperature ranges, an interior temperature of 22.5°C (72.5°F) and associated dynamic viscosity of air of 1.83×10-5 is assumed.
Initial flu particle diameters are taken from Table 1 in Yang and Marr (2011), based on the primary spreading event method selected – coughing, sneezing, or speaking. Geometric mean (GM) values from Duguid (1946) are used for these calculations based on Yang and Marr’s (2011) assessment of the “reliability of the methods and care and thoroughness of the experimental design and analysis” employed by Duguid (1946).
Equilibrium particle diameters were calculated using an average of the model based on experimentally derived respiratory droplet size transformation ratios give in Table 2, from Yang and Marr (2011). Settling velocities are calculated using the particle densities given in Sharp et al. (1945) and the Stokes Law formula given in Yang and Marr (2011).
Filter removal efficiency percentages are taken from droplet nuclei-weighted values given in Table 4 from Stephens (2012). The Influenza A virus inactivation rate is calculated from the linear equation given in Figure 2 from Yang and Marr (2011).
The Wells-Riley model is used to calculate estimates of the probability of infection, and this particular formula is taken from Stephens (2012). The Wells-Riley model has been around since the late 1970’s but modified some over the subsequent years. It’s “… based on a concept of ‘quantum of infection, whereby the rate of generation of infectious airborne particles (or quanta) can be used to model the likelihood of an individual in a steady-state well-mixed indoor environment being exposed to the infectious particles and subsequently succumbing to infection” (Stephens 2012:8).
While other types of models have subsequently been developed, such as dose-response (D-R) models, they all have their limitations. Stephens (2012) does acknowledge that further work should look at incorporating other models, but nevertheless chose to rely on a modification of the Wells-Riley model “in accordance with a long history of existing studies.” For this reason, these calculations are also based on the same modified Wells-Riley model. A value of 100 (Influenza A) is used for the quantum of infection (see Stephens 2012 for further information). While children typically shed virus at a greater rate than adults, the one value is used for both to simplify the process. Future updates may revise this.
A default value of 4.00 hours is provided for the exposure time per day, however this will vary quite a bit by a) facility type, b) the different occupants present in the facility, and c) the different activities they undertake during the day. If an infected individual is present in a room, the exposure time of elementary students could be significantly more than a typical office worker. It may be better to approach this as looking at a best-case (potential exposure of only 30 minutes or less) and worst-case scenario (potential exposure over the course of the entire work or school day).
The tool also accounts for the impacts of vaccination (or lack thereof). Default U.S. coverage rates for children and adults are provided based on averages of nine consecutive flu seasons for each, calculated from data provided by the CDC (Centers for Disease Control 2019). However, these averages hide a lot of variation by further age group breakdown and geographic location (for example the elderly typically vaccinate at a much higher rate than younger adults). You may want to consider fine tuning these percentages based on your building geographic location, occupant age groups, and other demographic factors.
To integrate the impact of vaccination into these calculations, we used the relationship between the probability of infection calculated by this tool and the basic reproduction number, R0. R0 is “… defined as the expected number of secondary cases produced by a single (typical) infection in a completely susceptible population” (Jones 2007), and the probability of infection is one of three factors multiplied by each other to calculate R0.
The impact of vaccination on the reproduction number can be estimated using the following formula: R0p = (1-p) * R0, where “where R0p is the R0 under vaccination and p is the vaccination coverage rate of the population who have been vaccinated” (Chen and Liao 2007:1039). We’re using the relationship between R0 and the probability of infection to estimate the impact of vaccination on the probability of infection, essentially multiplying it by (1-p). As vaccinations aren’t 100% effective, the p value for children and adults is also multiplied by estimates of vaccination effectiveness for children (0.70) and adults (0.62) provided by Chen and Liao (2013), respectively.
The number of infected individuals defaults to 1, but may be adjusted. More than one infected individual may have relevance for examining the probabilities of infection on a per hour or per day basis under different conditions. However, using a value greater than one could be problematic for exploring the probability of infection across a flu season. At this scale, one, two, more, or no infected individuals may be present on any given day or even any given hour over the course of the flu season. It’s more conservative to use one person and estimate the number of hours or percentage of time over the course of the flu season that at least one infected person may be present.
We’ve found it useful to try and back into that estimate. Tokars et. al (2018) found that on average 3% to 11% of the U.S. population is infected with the flu per flu season, resulting in actual symptomatic flu illness. If both symptomatic and asymptomatic illness is considered, that percentage ranges from 5% to 20%. To calculate a seasonal probability of infection that falls within the general realm of these percentages, the percentage of time exposed per flu season will need to be low, likely less than 10% or even less than 5% of an assumed five-month flu season (which in many cases probably makes sense). This is still the case even though the tool accounts for vaccinations, though the CDC default averages may be underestimating actual coverage. In the end, you’ll have to play around with this some. And remember that ultimately the delta between the design and baseline conditions is more important than either individual value.
The method of expelling flu particles – coughing, sneezing, or talking – determines the initial size and quantity of the flu containing droplets / aerosols, and therefore impacts the removal efficiencies and probability of infections. It also impacts the distance the particles are expelled from an infected individual, but these simple models do not take this into account when estimating removal efficiencies or probability of infections. You can play with the three different methods to see how it impacts your results.
Adult and Child pulmonary ventilation rates are determined using Table 6-31 (p. 6-67) from U.S. EPA (2011). The Total Daily IR (inhalation rate) value for an adult average, divided by 24 hours, was used to provide the adult pulmonary ventilation rate for these calculations, representing ages 18 and older. The Total Daily IR value for a 10-year-old child, divided by 24 hours, was used to provide the child pulmonary ventilation rate for these calculations, representing ages less than 18 years of age.
While all of the output should be viewed as results of a simplified model of reality, the probability of infection per flu season in particular should be viewed as a simple heuristic primarily useful for a relative comparison of the baseline and design conditions. In addition to the model’s simplifications being compounded over a longer period of time, the exposure time per flu season itself is difficult to estimate accurately, as discussed above.
Centers for Disease Control and Prevention (2019) Flu Vaccination Coverage, United States, 2018–19 Influenza Season. Accessed 06/12/2020. https://www.cdc.gov/flu/fluvaxview/coverage-1819estimates.htm
Chen, S. C., and C. M. Liao (2008) Modelling control measures to reduce the impact of pandemic inﬂuenza among schoolchildren. Epidemiology & Infection 136:1035-1045. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870896/
Chen, S. C., and C. M. Liao (2013) Cost-effectiveness of inﬂuenza control measures: a dynamic transmission model-based analysis. Epidemiology & Infection 141(12):2581-2594. https://www.cambridge.org/core/journals/epidemiology-and-infection/article/costeffectiveness-of-influenza-control-measures-a-dynamic-transmission-modelbased-analysis/983D7586168881E60C80B8614EA2E009
Duguid JP (1946) The size and the duration of air-carriage of respiratory droplets and droplet-nuclei. J Hyg 44: 471–479. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2234804/
Harper GJ (1961) Airborne micro-organisms: Survival tests with four viruses. J Hyg 59: 479–486. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2134455/
Jones, J. H. (2007). Notes on R0. Accessed on 06/12/2020. https://web.stanford.edu/~jhj1/teachingdocs/Jones-on-R0.pdf.
Keech M, Beardsworth P. (2008) The impact of influenza on working days lost. Pharmacoeconomics. 26(11):911–24. https://www.ncbi.nlm.nih.gov/pubmed/18850761
Sharp, D. G., A. R. Taylor, I. W. McLean, Jr., Dorothy Beard, and J. W. Beard. Densities and Sizes of the Influenza Viruses A (PR8 Strain) and B and the Swine Influenza Virus J. Biol. Chem. 1945 159: 29-. https://www.jbc.org/content/159/1/29.citation
Stephens, B. (2012) HVAC filtration and the Wells-Riley approach to assessing risks of infectious airborne diseases, Final Report. Prepared for The National Air Filtration Association (NAFA) Foundation. https://www.nafahq.org/wp-content/uploads/WellsRileyReport.pdf
Tokars, J., S. J. Olsen, C. Reed (2018) Seasonal Incidence of Symptomatic Influenza in the United States. Clinical Infectious Diseases. 66(10): 1511–1518. https://doi.org/10.1093/cid/cix1060
U.S. EPA, 2011. Exposure Factors Handbook: 2011 Edition (No. EPA/600/R-09/052F). National Center for Environmental Assessment, U.S. Environmental Protection Agency, Washington, DC. https://cfpub.epa.gov/ncea/risk/recordisplay.cfm?deid=236252
Yang W, Marr LC (2011) Dynamics of Airborne Influenza A Viruses Indoors and Dependence on Humidity. PLoS ONE 6(6): e21481. https://doi.org/10.1371/journal.pone.0021481
Additional Sources of Information
ASHRAE COVID-19 (Coronavirus) Preparedness Resources: https://www.ashrae.org/technical-resources/resources
ASHRAE Position Document on Infectious Aerosols: https://www.ashrae.org/file%20library/about/position%20documents/pd_infectiousaerosols_2020.pdf
ASHRAE Position Document on Airborne Infectious Diseases: https://www.ashrae.org/File Library/About/Position Documents/Airborne-Infectious-Diseases.pdf
REHVA COVID-19 Guidance: https://www.rehva.eu/activities/covid-19-guidance
AIA COVID-19 Resources for Architects: https://www.aia.org/pages/6280670-covid-19-member-resources-
AIA Re-Occupancy Assessment Tool: https://www.aia.org/press-releases/6292741-architects-release-new-resource-for-safer-
COVID-19: A Path Forward (Harvard T.H. Chan School of Public Health, Center for Communicable Disease Dynamics, and Healthy Buildings): https://covidpathforward.com/
Ten Facts about UV Radiation and COVID-19: https://www.tandfonline.com/doi/full/10.1080/15502724.2020.1760654
IES Committee Report: Germicidal Ultraviolet (GUV) – Frequently Asked Questions: https://www.ies.org/standards/committee-reports/
CIE 155:2003 Technical Report – Ultraviolet Air Disinfection: http://files.cie.co.at/cie155-2003%20(free%20copy%20March%202020).pdf
Viruses in Droplets and Aerosols Presentation, by Dr. Linsey Marr, Charles P. Lunsford Professor of Civil and Environmental Engineering at Virginia Tech: https://www.youtube.com/watch?v=dD1gKaaQg6k&feature=yout
How can airborne transmission of CoV-2 indoors be minimized presentation, by Dr. Shelly Miller, Professor of Mechanical Engineering at the University of Colorado Boulder and faculty member of the Environmental Engineering Program: https://www.youtube.com/watch?v=jK6Cef5A8FQ&feature=youtu.be
Managing HVAC Systems to Reduce Infectious Disease Transmission presentation, by Dr. Bill Bahnfleth, professor and director of the Indoor Environment Center in the Department of Architectural Engineering at The Pennsylvania State University: https://betterbuildingssolutioncenter.energy.gov/webinars/managing-hvac-systems-reduce-infectious-disease-transmission
Airborne, Droplets, and HVAC presentation, by Travis English, PE, CEM, LEED AP, Engineering Manager for Kaiser Permanente (KP) National Facilities Planning group, and KP’s designated Chief Engineer of Design Excellence: https://www.youtube.com/watch?v=_3K-w_ZGXBM&feature=youtu.be
Weighted Average Salary Sources (U.S.)
Employment Cost Trends: http://www.bls.gov/ncs/ect/home.htm – Provides wages/salaries and benefits by industry, demographic, region, etc.
FederalPay.org – Government Pay Tables, Calculators, and More Federal: https://www.federalpay.org/
General Schedule (GS) Payscale Table for 2020: https://www.federalpay.org/gs/2020
Salary Comparison and Salary Calculator: http://about.salary.com/