We built a decision-analytic model that is designed to assist local and federal regulators in setting standards for improving the air handling systems in poorly ventilated indoor commercial spaces for the prevention of SARS-CoV-2 infections via aerosolized particles. The model is designed to compute the incremental cost-effectiveness ratio (ICER), which is the net cost of an intervention divided by the number of quality-adjusted life years (QALYs) gained (14). The ICER can be used to compare commonly deployed health or medical interventions to assess whether they are affordable (15, 16). We followed guidelines for conducting our cost-effectiveness analyses (17), including estimation of costs from a societal perspective. We based our analysis on a standardized space for the purposes of this paper but provide an online interface for customization to most spaces.
Characteristics of the standardized space: Each restaurant, café, or bar is unique with respect to the size, number of customers, hours of operation, and the time that customers spend in the establishment. This variation presents challenges for understanding the airflow and filtration needs for any given business. For this reason, we developed a customizable interface that allows both regulators and restaurant owners to obtain estimates for a range of settings (https://openupuniversities.shinyapps.io/Airborne_Transmission_Covid19/). In this paper, we used a small, poorly ventilated restaurant space as an example so that the reader can get a general idea of the cost-effectiveness of standalone ventillation.
The standardized restaurant was open for a total of 3 hours for lunch service and 6 hours for dinner service. We assumed that the restaurant has a seating capacity of 30 occupants in a 1,000 square foot space and a ceiling height of 9 feet, and that each occupant is seated for one-hour at lunch and 1.5-hours during dinner. The model assumptions are listed in Table 1.
Table 1
Model assumptions for evaluating the cost-effectiveness of improving ventilation in commercial spaces for the prevention of SARS-CoV-2.
Assumptions
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The standardized room of 1000 square-foot with a ceiling height of 9 feet has 0.8 air changes per hour, primarily from the door opening and closing and the food vent running.
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For lunch, the restaurant is open for 3 hours. Each of 30 occupants is seated for one hour. We modeled 3 consecutive lunch events each for a duration of 1 hour. In each event, the restaurant is at the full seating capacity.
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For dinner, the restaurant is open for 6 hours. Each of 30 occupants is seated for 1.5 hours. We modeled 4 consecutive dinner events each for a duration of 1.5 hours. In each event, the restaurant is at the full seating capacity.
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Between lunch and dinner hours, the restaurant is closed for enough time so that the virus concentration in the indoor air dropped to zero as workers opened doors and moved throughout the space.
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The restaurant is operating 7 days a week with similar lunch and dinner hours.
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The model is built under well-mixed conditions for an infected individual present in an indoor space and there is dynamic airflow in unpredictable patterns associated with the movement of people and an overhead fan (18,19).
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We assumed that transmission through the close-range mode—that is, when infectious aerosols were inhaled directly from the exhaled breath of an infected individual by a susceptible person in its vicinity—is on par between the comparison arms. Thus, only infection through the inhalation of accumulated aerosols, often referred to as the long-range mode of airborne transmission, is modeled and close-range transmission is not modeled (18,19).
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We assumed that infected symptomatic Covid-19 cases would quarantine for 14 days. We also assumed those infected cases who required hospitalizations would quarantine for 21 days.
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All wages were valued at the median hourly wage in the US (14).
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US: United States. |
Temporal evolution of concentration of viable viral copies in an indoor space: In a previous published work, two co-authors developed a model (18) and online tool (19) for the temporal concentration of aerosolized viral copies in the air under well-mixed conditions for an infected individual present in an indoor space. The model considers the evaporation and settling of virus-laden droplets of various sizes exhaled by an infected individual in terms of plaque forming units (PFUs). These are evaluated from a combination of reduced-order modeling and previous experimental measurements. The details are described elsewhere (18). In brief, the concentration of PFUs dispelled by an infected person in an indoor space can be shown as
\(C\left(t\right)={n}_{inf}.\frac{{N}_{gen}}{V.(\lambda +\kappa +\nu )}+\left(C\left({t}_{0}\right)-{n}_{inf}.\frac{{N}_{gen}}{V.\left(\lambda +\kappa +\nu \right)}\right).\text{e}\text{x}\text{p}(-\left(\lambda +\kappa +\nu \right).(t-{t}_{0}\left)\right)\) , where:
\(C\left(t\right):\) concentration of viral PFUs over time and \(C\left({t}_{0}\right)\) represents the concentration at baseline;
\({n}_{inf}:\) number of infected individuals in the room;
\({N}_{gen}:\) generating factor for viral particles emitted by continuous exhalation of the infected person while speaking per time unit. The generating factor of 0.059 PFU/second (18) was estimated using a viral load at the sputum of the infected person of 10^10 virus RNA copies/ml. While the mean virus RNA copies/ml of the infected sputum for the original strains of Covid-19 was estimated as 7*10^6 (20), the emerging evidence shows that the number of viral copies is almost 1,000 times larger for the Delta variant (21), the most common Covid-19 strain at the time of publication. Therefore, to be conservative, we assumed a 10^10 virus RNA copies/ml for the Delta variant. We then applied a conversion factor of 0.01 to estimate PFUs (infectious units) from RNA copies (18). Here, the aerosol cut-off diameter—the size below which particles are carried by the ventilation air flow—was assumed to be 20 µm. The exhalation flow rate was assumed to be 0.211 liters/second representing a sedentary activity (18);
\(V:\) Volume of the room. We showed our analysis for a 1000 ft2 restaurant area size with a ceiling height of 9 ft;
\(\lambda :\) Natural viral decay rate. An exponential decay at a rate of 0.636 per hour was assumed (22);
\(\kappa :\) Settling rate of aerosols by gravity. A value of 0.39 per hour was assumed (18); and
\(\nu :\) ventilation rate of the room per air changes per hours (ACH).
Risk of infection in an indoor space through long-range transmission of airborne, aerosolized SARS-CoV-2 particles: For an average susceptible individual sitting in the restaurant, we calculated the risk of SARS-CoV-2 infection based on the number of viral PFUs that the individual is exposed to for the duration of a lunch event (1 hour) or a dinner event (1.5 hours). A susceptible individual is defined as a person who is disease-free at the start of lunch or dinner service and is at risk of contracting the disease while sitting in the restaurant. We assumed that if people are sitting in the restaurant for an event, based on the prevalence of disease in the surrounding community (denoted by ), there would be, on average, infected individuals and susceptible individuals for that event. We calculated the number of PFU units that a susceptible individual is exposed to during an event (denoted by ) as follows
\({nPFU}_{exposed}={\int }_{{t}_{1}}^{{t}_{2}}{N.Pr.C}_{PFU}\left(t\right).Inhalation\_rate.dt\) , where:
\({t}_{1}\) and \({t}_{2}:\)represents respectively the starting and ending time of the event;
\(N.Pr:\) represent the average number of infected people in the event;
\({C}_{PFU}\left(t\right):\) represents the temporal concentration of viral PFU units (see the section “Temporal evolution of concentration of viable viral copies”); and
\(Inhalation\_rate\) : Inhalation rate of 0.521 liters/second for an average person with a sedentary activity person (e.g., sitting and speaking) (23).
We calculated the risk of infection (denoted by \({p}_{inf}\)) for an average individual based on the number of viral PFUs the individual is exposed to during an event as follows:
$${p}_{inf}=1-{\left(1-{p}_{d}\right)}^{{nPFU}_{exposed}}$$,
where \({p}_{d}\) represents the probability of infection per exposure to one viral PFU. We calculated \({p}_{d}\) as 0.0024 (95% Confidence Interval [CI]: 0.0013-0.0053) based on an infectious dose 50 (ID50) of 280 (95% CI: 130-530) PFUs (18, 24). The ID50 indicates the number of viral particles required to cause infection in 50% of the individuals exposed to these particles.
The above modeling approach considers only infection through the inhalation of accumulated aerosols, often referred to as the “long-range” mode of airborne transmission. Thus, transmission through the close-range mode—that is, when infectious aerosols were inhaled directly from the exhaled breath of an infected individual by a susceptible person in its vicinity—was assumed to be on par between the comparison arms and was disregarded.
Costs: We modeled the cost of installing standalone air filtration units with HEPA filters, which trap ultrafine particles down to the sub-micrometer size (11). Based on the restaurant’s size and cubic feet per minute (CFM) airflow of the standalone units, we calculated the number of units required to produce the equivalent of 12 ACH in the room. These units were assumed to be uniformly installed in the room to create different points of air disturbance.
We modeled direct and indirect costs of hospitalizations due to Covid-19 (25, 26). For indirect costs of hospitalizations, we assumed a 21-day absence from work spanning the time spent in the hospital time spent at home after hospital discharge. We assumed 8 hours of work lost per day at a value of $25/hour (27). We assumed a 14-day quarantine for symptomatic infections for lost productivity and leisure time of 8 hours per day. Future values were discounted at 3% (14, 17). All costs were adjusted to 2020 US dollars (Table 2).
Table 2
Model input parameters for evaluating the cost-effectiveness of improving ventilation in commercial spaces for the prevention of SARS-CoV-2.
Parameter
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Base case value
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Probability distribution
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Number of people sitting in the restaurant at once
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30
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Linear
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Average age of the people sitting in the restaurant
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45
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(Changed in the sensitivity analysis from 35-55)
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Probabilities and rates
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Probability of infection for one PFU unit exposed (based on ID50 of 280 (95% CI: 130-530) PFU units) (18,24)
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0.0024
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Beta (15.9592, 6633.707)
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Proportion of asymptomatic cases among all exposed people (excluding the ones initially asymptomatic but became symptomatic eventually) (39)
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0.25
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Beta (18.5, 55.5)
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Probability of long Covid-19 among symptomatic cases (40)
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0.133
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Beta (86.567, 564.3127)
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Infection hospitalization rate (37)
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Age-dependent:
0.019 for the average age of 45 years old
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Beta (98.081, 5064.077)
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Infection mortality rate (28)
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Age-dependent:
0.001 for the average age of 45 years old
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Beta (99.899, 99799.1)
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Relative rate of symptomatic infection with Delta among the fully vaccinated (relative rate of 0.22 is equivalent of 78% reduction in symptomatic infection; the value represents the average effectiveness of the BNT162b2 and ChAdOx1 nCoV-19 vaccines against Delta variant) (41)
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0.22
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Beta (14.8808, 52.7592)
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Direct costs (U.S. dollars in 2020 USD)
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Improving room ventilation rate to 12 ACH (by installing 5 standalone air filtration units with HEPA filters trapping ultrafine particles down to the sub-micrometer size that are uniformly installed in the room and produce an equivalence of 12 ACH for a 1000 ft2 space (each unit produces an airflow of 347 CFM and costs $750) (42)
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$3,750
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Gamma (100, 0.02667)
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Covid-19 hospitalization (25,26)
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$23,489
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Gamma (100, 0.00426)
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Indirect costs (U.S. dollars in 2020 USD)
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Covid-19 infection without hospitalization for symptomatic cases (losses of productivity over 2 weeks of self-isolation)
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$2,800
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Gamma (100, 0.036)
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Covid-19 hospitalization (losses of productivity over 3 weeks)
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$4,200
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Gamma (100, 0.024)
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Premature mortality due to Covid-19 (calculating losses of annual average wage of $50,000/year beyond the age at death of 45 years old in the base case model until the age of 65 years; future values were discounted at 3%)
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$793,874
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Gamma (100, 0.000126)
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Health-related quality of life
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Losses of QALYs associated with a Covid-19 symptomatic case (28)
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0.008
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Beta (99.192, 12299.81)
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Losses of QALYs associated with a long Covid-19 infection (28)
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0.034
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Beta (96.566, 2743.61)
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Losses of QALYs associated with a Covid-19 hospitalization (28)
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0.020
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Beta (97.970, 4776.154)
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Losses of QALYs associated with a Covid-19 death (calculated based on an average age of 45 years at death, life expectancy of 80 years, age-dependent QALYs of the US general population, and discounting future values at 3%) (29)
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18.33
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Normal (18.33, 1.83)
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iD50: infectious dose 50; CI: confidence interval; PFU: plaque forming unit; ACH: air changes per hour; HEPA: High Efficiency Particulate Air; CFM: cubic feet per minute (to measure airflow); QALY: quality adjusted life year. |
Health-related quality of life: We modeled losses of QALYs associated with a Covid-19 symptomatic infection and Covid-19 hospitalization (28). A QALY is a metric capturing both longevity and health-related quality of life (HRQL). A QALY can be conceptualized as a year of life lived in perfect health and is calculated as the product of the life years remaining and the HRQL score. We also modeled changes in QALYs for the proportion of infected individuals who suffer from long-haul Covid-19 symptoms (28). Finally, we modeled losses of QALYs associated with a Covid-19 premature death (29). We discounted future values at 3% (14, 17).
Analysis: We compared two interventions: 1) no improvement in the baseline ventilation rate of 0.8 ACH (‘status quo’), and 2) improving the room ventilation rate to 12 ACH. Our mathematical model was probabilistic and was developed in a Monte Carlo simulation of 1,000 iterations, with each iteration randomly drawing from probability distributions of the input parameters. Table 2 shows the model inputs along with their probability distribution.
We performed our analyses for different conditions defined by the mean year-round prevalence of actively infectious cases in the surrounding communities where the restaurant is located and the proportion of patrons that are vaccinated. For the base case model, we assumed a 1% mean year-round prevalence of actively infectious cases in the surrounding community and a 50% full-vaccination rate among customers sitting in the restaurant. We modeled the random daily incidence rate from a normal distribution and summed the daily incidence rates over the past 12 days to obtain the daily prevalence of actively infectious cases. This assumes an average of 12 days of infectiousness for an exposed individual beginning 2 days prior to symptom onset (for symptomatic cases) plus 10 days following the initial symptom onset (30, 31).
For the best-case scenario (minimum number of infections), we assumed a year-round prevalence of actively infectious cases of 0.1% in the surrounding community and a 70% full-vaccination rate among customers sitting in the restaurant.
For the worst-case scenario (maximum number of infections), we assumed a year-round prevalence of actively infectious cases of 2% in the surrounding community and a 0% full-vaccination rate among customers sitting in the restaurant.
The time horizon of the model was one year. The outcomes of the model were incremental direct and indirect costs, infections averted, QALYs gained, and ICER for improving the ventilation rate. We also conducted one-way sensitivity analyses over all core input parameters of the model to measure the robustness of model outcomes against changes in these parameters.