Relative Risk Reduction Method in Ventilation Design for Airborne Transmission

Key words: ventilation, airborne transmission, viruses

The importance of reducing airborne transmission of viruses in shared indoor spaces is well understood but common understanding how ventilation design should contribute develops slowly. Possible design methods discussed in the revision of EN 16798-1:2019 standard are benchmarked in this article.

To consider airborne transmission of viruses in ventilation design, methods either being based on absolute or relative infection risk can be used. Most common is the standard airborne disease transmission Wells-Riley model where the viral load emitted by infector is expressed in terms of the quanta emission rate and the absolute probability of infection can be calculated. Such design method [1] is proposed to be included in the ongoing revision of EN 16798-1:2019 standard in CEN TC 156 WG25. However, it is known that the core input data for this method, quanta emission rates have large variations [2] and are difficult to quantify.

Alternatively, relative risk reduction method can be used, making it possible to calculate the risk reduction from the initial/reference case conditions without any uncertainty related to the viral load. For instance, if sick leave or disease cases data is available for a specific building, it can be calculated how much the ventilation would have been needed to be increased to reduce the number of disease cases by certain amount. For instance, relative risk reduction by 80%, (R1 − R2) / R1 = 0.8 corresponds to relative risk R2/R1 = 0.2. In similar fashion the impact of room air cleaners, UV devices or reduced occupancy can be calculated. It should be noted that this method allows to calculate the relative risk reduction explicitly, but the initial infection probability and number of disease cases cannot be calculated.

Relative risk reduction method

Target ventilation rate independent on the viral load and providing a specified relative risk from the reference ventilation rate and number of persons can be calculated [3]:

where

λ2        total removal rate corresponding to specified relative risk r in case 2, m³/h

λ1        total removal rate in the reference case 1, m³/h

Ns2      number of susceptible persons in the room in the target ventilation case 2, -

Ns1      number of susceptible persons in the room in the reference case 1, -

r          relative risk r = R2/R1 where R1 and R2 are number of new disease cases in the reference and target cases 1 and 2, -

Total removal rate is defined as:

where

Q         ventilation rate (m³/h)

λdep     deposition onto surfaces (1/h)

k          biological decay rate (1/h)

kf         filtration by a portable air cleaner (1/h)

kUV      disinfection by upper room ultraviolet germicidal irradiation UVGI (1/h)

V         volume of the room (m³)

In the case of recirculation, Q is the sum of outdoor and non-infectious recirculated supply airflow rate. In [3] practical equation has been derived allowing to calculate relative risk reduction from the reference case by changing the number of occupants, ventilation rate and removal rates by room air cleaner and UV. While Q1 refers to the reference/initial case, new ventilation rate Q2 in case 2 from Eq. (1) becomes:

where

Q2        target ventilation rate corresponding to specified relative risk r in case 2, m³/h

Q1        ventilation rate in the reference case 1, m³/h

In the case of no air cleaner and no UVGI, one infectious person assumption, and with values of 0.24 1/h for deposition loss rate and 0.63 1/h for virus decay, Eq. (3) becomes in L/s units:

where

Q2        target ventilation rate corresponding to specified relative risk r in case 2, L/s

Q1        ventilation rate in the reference case 1, L/s

N2       number of persons in the room in the target ventilation case 2, -

N1       number of persons in the room in the reference case 1, -

r          relative risk compared to reference case 1 with r = 1, -

In Eq. (4), the only virus specific term is the biological decay rate, for which roughly the same value applies both for SARS-CoV-2 and influenza [4]. Eq. (4) may be used to calculate the target ventilation rate providing a specified risk reduction from the lowest possible ventilation rate of Category IV, that will be then considered as the reference case 1. Relative risk to be achieved can consider activities with higher virus emission rates such as speaking and physical activities. Default target values in ventilation design for some space categories proposed in [3] are given in Table 1.

Table 1. Default target values in ventilation design for relative risk compared to Category IV risk level (relative risk reduction is 1 − r) and quanta parameter for absolute risk Eq. (5).

Application

Ventilation rates needed for the relative risk reduction are compared in the following to those calculated with absolute risk based equation recommended in the revision of EN 16798-1. Absolute risk based target ventilation rate for the breathing zone combines the ventilation to dilute the viral load and removal by other mechanisms than ventilation calculated with the steady state equation derived in [1]:

where

Q         target ventilation rate for the breathing zone, L/s

qq        quanta emission specific ventilation rate for occupancy per person (Table 1), L/(s person)

qr        removal rate of virus decay, deposition, air filtration and disinfection, 0.24 L/(s m³) for deposition and decay L/(s m³)

N         design value for the number of persons in the room with the distancing >1.0 m to avoid close proximity

V          room volume, m³

Five model rooms are specified in Table 2 to calculate the target ventilation rates with Eq. (5) and to compare with relative risk reduction calculated from Eq. (4). For the meeting room, restaurant and fitness, 50% of occupancy is considered to enable to follow >1 m distancing requirement, i.e. the number of persons is 12, 28 and 17 when calculated with Eq. (5). While in the classroom and open plan office, infection risk-based target ventilation rates are almost equal with Category II ventilation rates, the values are higher in other rooms showing the effect of higher quanta value.

Table 2. Calculation example of infection-risk based target ventilation rate that is compared with Category I and II perceived air quality ventilation rates.

¹ 50% of occupancy is used in the infection risk based target ventilation rate calculation.

Relative risk reduction compared to Category IV ventilation rate is calculated for the same rooms with Eq. (4), Figure 1a. Category IV ventilation rate is 4.0 L/s per person in the classroom, meeting room and restaurant, 4.1 L/s per person in the fitness and 5.8 L/s per person in the open plan office. In the open plan office, the occupant density is much lower compared to other rooms that leads to slower risk reduction when increasing ventilation rate.

Infection risk-based target ventilation rates in Table 2 correspond to relative risk of 0.55 and 0.59 in the classroom and office, Figure 1a. In this figure, all rooms are calculated with full occupancy differently from Table 2, that results to relative risk of about 0.3 in the meeting room, restaurant and fitness.

In addition to ventilation rate, relative risk allows to assess the impact of reduced occupancy. Results with 50% occupancy in the meeting room, restaurant and fitness (as in Table 2) and 80% occupancy in the open plan office are shown in Figure 1b where ventilation rate per person is shown as per initial number of persons. 50% occupancy has led to remarkable risk reduction as r = 0.2 is achieved with 12 L/s per person. In these cases, as low as r = 0.15 corresponds to infection risk based ventilation rates. This shows that relative risk of 0.5 that is achieved with reasonable ventilation rates in the classroom and office will not serve as design criterion in other rooms. Therefore, lower relative risk values of about 0.15 might be appropriate for the meeting room, restaurant and fitness, because the absolute risk corresponding to initial r = 1 is higher in rooms with higher viral load.

Figure 1. Relative risk to Category IV ventilation rate (r = 1). a) Occupancy not changed. b) With reduced occupancy in the meeting room, restaurant and fitness (-50%) and in the office (-20%).

Relative risk is sensitive to occupant density because even if not changed the number of persons is included in Q1 and the room volume is included too in Eq. (4). To show the sensitivity, the classroom and office cases were calculated with three occupancy values corresponding to medium, low and high occupant density in these rooms, Figure 2. In the classroom, changes close to a typical occupancy of 2 m² per person had a small impact as 1.5 m² and 2.2 m² per person curves are close to each other and infection risk-based ventilation rates calculated with Eq. (5) for medium and high occupancy of 8.0 and 8.6 L/s per person correspond to relative risk of 0.58 and 0.52. In the office, where occupant densities are lower, the impact of higher room volume per person increases differences. In this case, infection risk-based ventilation rates 14.8, 18.5 and 8.0 L/s per person for medium, high and low occupancy, calculated with equation 5, correspond to considerably different relative risk values of 0.59, 0.37 and 1.03. Contrary to the infection risk-based ventilation rate, relative risk provides the lowest value at high occupancy followed by medium and low occupancy.

If for instance r = 0.5 would be used as design criterion, low occupancy ventilation rates which are high per person are not a problem, because the total airflow rate would be smaller than that calculated with medium occupancy values. Therefore, the only problematic case would be an office with really high occupant density, in which case the required ventilation rate might be underestimated.

Figure 2. Relative risk sensitivity to occupant density. a) classroom with 25, 37 and 11 persons (2.2, 1.5 and 5.1 m² per person). b) office with 22, 40 and 12 persons (11.0, 6.1 and 20.2 m² per person).

Conclusions

Relative risk reduction method could complement an existing perceived air quality method in EN 16798-1:2019 standard so that a lowest possible Category IV ventilation rate is used as a reference case. Results show that relative risk of 0.5 is achieved with reasonable ventilation rates in the classroom and office, but in other rooms even higher reduction, relative risk of about 0.15 (=85% reduction), might be reasonable design criteria for the target ventilation rate.

When applied for design with fixed relative risk value the method provided the lowest ventilation rate per person at highest occupant density that is not logical. This may underestimate the required ventilation rate in rooms with high occupant density. It is concluded that the method should not preferred for ventilation design because the quanta method proposed to EN 16798-1 revision is capable to handle occupant density variations in correct fashion.

Relative risk reduction method may be useful for existing buildings because it is possible to calculate the risk reduction from the initial case conditions without any uncertainty related to the viral load. For instance, if sick leave or disease cases data is available for a specific building, it can be calculated how much the ventilation would have been needed to be increased to reduce the number of disease cases to a specified level. It can be also used to refine critical parameters in the quanta method.

References

[1]     Kurnitski J., Kiil M., Mikola A., Võsa K.V., Aganovic A., Schild P., Seppänen O. Post-COVID ventilation design: Infection risk-based target ventilation rates and point source ventilation effectiveness. Energy and Buildings, Volume 296, 2023, 113386 https://doi.org/10.1016/j.enbuild.2023.113386

[2]     Benjamin Jones, Christopher Iddon, Max Sherman, Quantifying quanta: Determining emission rates from clinical data, Indoor Environments, 2024, https://doi.org/10.1016/j.indenv.2024.100025

[3]     Jarek Kurnitski, Martin Kiil, Amar Aganovic, Bjarne Olesen. Relative Risk Reduction in Ventilation Design for Airborne Transmission, Proceedings of the 15th REHVA HVAC World Congress CLIMA 2025, Volume 2, pp. 723–732, https://doi.org/10.1007/978-3-032-06810-1_72

[4]     Aganovic, A., Bi, Y., Cao, G. et al. Modeling the impact of indoor relative humidity on the infection risk of five respiratory airborne viruses. Sci Rep 12, 11481 (2022). https://doi.org/10.1038/s41598-022-15703-8