Upper-room ultraviolet air disinfection might help to reduce COVID-19 transmission in buildings: a feasibility study

Theory

At any point in time the amount of viral inactivation (disinfection) achieved for a given UV radiant flux (irradiance) can be described using the following first order decay equation (McDevitt, Rudnick & Radonovich, 2012).

(1) $$N_t=N_0\times e^{-Z.E.t}$$where: N₀ and N_t are the number of viable viral particles (virions) at time zero and t seconds respectively; Z is the UV susceptibility constant for the virus (m²/J); E is the radiant (irradiation) flux (W/m²); and t is time in seconds.

The UV irradiation dose received by the virus is simply: (2) $$H=E\times t$$where: H is the observed UV irradiation dose (J/m²).

By combining Eqs. (1) and (2), and rearranging we can obtain a value for Z.

(3) $$Z=-{\displaystyle \frac{1}{H}\times \ln \left({\displaystyle \frac{N_t}{N_0}}\right)=-{\displaystyle \frac{1}{H}\times \ln \left(f\right)}}$$where: f is the survival fraction.

Because the relationship between the UV dose and the natural logarithm of the survival fraction is broadly linear for most viral species, it means that the behavior of any given virus exposed to UV-C light can be succinctly described by the value of Z, irrespective of the actual UV dose applied. As such, for any given viral species, if the value of Z is known, then it should be possible to predict with reasonable accuracy how the virus will behave when exposed to a given UV-C dose in any context. Microbes that exhibit larger Z values are more susceptible to UV damage, whereas those with small Z values are more difficult to inactivate.

UV inactivation plots for most viral species tend to be straight lines, although some might exhibit a curve (Kariwa, Fujii & Takashima, 2006). Notwithstanding this, the model described in Eq. (1) is still a good approximation for most viral species (McDevitt, Rudnick & Radonovich, 2012) up until the point where the “target” becomes saturated with UV photons. At this point, because all the virions have already been inactivated, increasing the UV dose further has no effect and so the linear relationship between UV dose and the log reduction becomes decoupled, with the result that the Z value no long applies.

Instead of quantifying UV inactivation in terms of survival fraction, many researchers, particularly those working in biology, describe the reduction in the microbial count in terms of log reduction, which can be converted to survival fraction as follows: (4) $$f={\displaystyle \frac{1}{{10}^A}}$$where: A is the log₁₀ reduction in the number of virions.

Specifically, with regard to upper-room UVGI, once the Z value has been obtained for the target microbe, it is then possible to determine the irradiation flux required to disinfect it, using the methodology described in Beggs & Sleigh (2002). This method makes the assumption that the room air is well mixed, which is a reasonable approximation for most applications (Beggs & Sleigh, 2002). If this is the case, then the average particle residence time, t_res (in seconds) in the room space will be: (5) $$t_{\mathrm{r}\mathrm{e}\mathrm{s}}={\displaystyle \frac{1}{n}\times 3600}$$where: n is the room ventilation rate in air changes per hour (AC/h).

From Eq. (5) it can be approximated that the average particle residence time in the upper-room UV field, t_uv (in seconds) will be: (6) $$t_{\mathrm{u}\mathrm{v}}=t_{\mathrm{r}\mathrm{e}\mathrm{s}}\times {\displaystyle \frac{h_{\mathrm{u}\mathrm{v}}}{h_r}}$$where: h_r is the floor-to-ceiling height (m), and h_uv is the depth of the upper-room UV zone (m) (see Fig. 1).

Because Z values are often determined experimentally using microbes suspended in liquids or on surfaces, it may be necessary to adjust the Z value for use with upper-room UVGI systems (Beggs et al., 2006; Yang et al., 2017), as follows: (7) $$Z_{\mathrm{u}\mathrm{r}}=Z\times c_{\mathrm{u}\mathrm{r}}$$where: Z_ur is the effective upper-room Z value (m²/J), and c_ur is a correction coefficient.

For practical purposes, Z_ur can be assumed to be the same as the Z value achieved when a given microbe is irradiated in an aerosol.

So if we assume that the air in a room is well mixed, by combining Eqs. (2), (3) and (6) it is possible to compute the average irradiation flux, E_r, that is required to achieve a desired survival fraction, f_r.

Alternatively, the disinfection achieved by an upper-room UVGI system can be thought of as being equivalent to additional air changes in the room space (McDevitt et al., 2008). In this scenario, the UV rate constant, k_uv, which can be thought of as the equivalent air change rate per second, can be determined using (Beggs et al., 2006): (9) $$k_{\mathrm{u}\mathrm{v}}=Z_{\mathrm{u}\mathrm{r}}\times E\times {\displaystyle \frac{h_{\mathrm{u}\mathrm{v}}}{h_r}}$$

So, in a ventilated room in which contamination ceases at time zero, we can utilize both the UV rate constant, k_uv, and a rate constant, k_v, for the ventilation (i.e., n ÷ 3,600), to produce a decay model for the room space.

(10) $$C_t=C_0\times {\mathrm{e}}^{-\left(k_v+k_{\mathrm{u}\mathrm{v}}+k_d\right)t}$$where: C₀ and C_t are the concentrations of viable viral particles in the room space (virions/m³) at time zero and t seconds respectively; k_v is the ventilation rate constant; k_d is the particulate deposition rate constant (e.g., 0.0014 s⁻¹ (Stadnytskyi et al., 2020)); and t is time in seconds.

Analysis of published data

A search of the relevant scientific literature (i.e., published literature, pre-prints and relevant websites) was undertaken to identify published data relating to the UV irradiation of the three closely related coronaviruses: SARS-CoV-2, the causative agent of COVID-19; SARS-CoV-1, the causative agent of severe acute respiratory syndrome (SARS); and MERS-CoV, the causative agent of middle east respiratory syndrome (MERS).

Because the experimental methods used in the various UV studies varied greatly, as did the level of detail reported, it was necessary to adopt a standardized approach so that valid comparisons could be made. It was therefore decided that, rather than estimating the Z value for a nominal log one reduction (i.e., D₉₀) as others have done (Kowalski, 2010), we would instead use the log reduction values and UV doses reported in the various studies to calculate the respective Z values using Eq. (3). In so doing, we were able to utilize the results from studies that would otherwise be excluded because the log reductions achieved were far in excess of one. Where researchers performed experiments using a range of UV doses, we calculated the Z value for two UV doses, one near the start of the inactivation process and the other just before the saturation point. So as to avoid bias due to pseudo-replication, when computing the average Z values for the respective viral species, we first aggregated the Z values reported for the various individual studies and then used the aggregated values to calculate the overall mean Z values for the respective viruses.

In order to compare the Z values for the coronaviruses with those for influenza, we utilized experimental results produced by Heimbuch & Harnish (2019) who irradiated coupons of respirator material inoculated with SARS-CoV-1 and MERS-CoV, as well as four strains of influenza A, allowing direct comparisons to be made between the viral species.

Estimating an effective upper-room Z value for aerosolised SARS-CoV-2

In order to evaluate how SARS-CoV-2 might behave in the presence of UV-C when aerosolised, we reviewed the available literature on the subject (Jensen, 1964; Kowalski, 2010; Kowalski et al., 2000; McDevitt, Rudnick & Radonovich, 2012; Walker & Ko, 2007) with the aim of estimating a value for the coefficient, c_ur, in Eq. (7), which we then used to estimate the effective upper-room Z value, Z_ur. In order to reflect the uncertainty associated with this, we compared effective Z values for aerosolised coronaviruses reported in the literature with values obtained for SARS-CoV-2 in liquids to obtain the range of possible values for c_ur.

Computation of required upper-room UV irradiation flux

Having estimated the value of Z_ur for SARS-CoV-2 from the literature, we then used Eqs. (6) and (8) to estimate the average upper-room irradiation flux that would be required to achieve a 50–90% reduction in aerosolised SARS-CoV-2 virions (through the action of the UV-C alone) in a 4.2 × 4.2 × 2.5 m high room space for a range of ventilation rates. These dimensions were chosen because they are typical for an upper-room UVGI installation in which the lamp height is 2.1 m above the floor (First et al., 1999b). In the model we assumed that the air was completely mixed, which meant that according to Eq. (6), aerosol particles would spend on average 16% of their room residency time in the UV zone.

In addition to computing the required UV flux, we also wanted to know how a standard upper-room UV fitting might perform when challenged by SARS-CoV-2. In accordance with the guidelines stated by First et al. (1999b), we assumed that the room contained a single 30 W (input) UV-C fitting capable of delivering an average upper-room flux of 50 μW/cm², and modeled its performance in terms of equivalent ventilation rate using Eq. (9).

Analysis of the published literature

The results of the literature search are summarized in Table 1, which shows the UV-C (254 nm) doses applied and log reductions achieved in six studies investigating SARS-CoV-1 (Darnell et al., 2004; Darnell & Taylor, 2006; Duan et al., 2003; Eickmann et al., 2020; Heimbuch & Harnish, 2019; Kariwa, Fujii & Takashima, 2006), two studies investigating MERS-CoV (Bedell, Buchaklian & Perlman, 2016; Heimbuch & Harnish, 2019), and two studies investigating SARS-CoV-2 (Bianco et al., 2020; Signify, 2020). Table 1 also includes the results of one study that investigated the impact of deep-UV light at 280 nm (i.e., the boundary between UV-B and UV-C) on SARS-CoV-2 (Inagaki et al., 2020). In addition, three studies were found that used a combination of UV-A and UV-B light (270–360 nm), together with the photosensitiser, riboflavin, to disinfect SARS-CoV-2 (Keil et al., 2020; Ragan et al., 2020) and MERS-CoV (Keil, Bowen & Marschner, 2020) in blood products (Table 2). Although these studies did not utilize UV-C light, it was nevertheless decided to report the results of these studies here so that direct comparisons could be made between SARS-CoV-2 and MERS-CoV. The MERS-CoV irradiation study by Bedell, Buchaklian & Perlman (2016) is included for completeness, even though the authors did not report the UV dose received by the virus, making it impossible to compute a Z value for this study.

The computed Z values for the respective experiments are shown in Table 3 (UV-C and deep-UV) and Table 4 (UV-A/B plus riboflavin). From these it can be seen that the Z values for the MERS-CoV virus were similar in magnitude to those for both SARS-CoV-1 (UV-C) and SARS-CoV-2 (UV-A/B). With UV-C irradiation the mean Z value for SARS-CoV-1 was 0.00489 (SD = 0.00611) m²/J, whereas that for MERS-CoV was 0.00104 m²/J. Likewise, for UV-A/B plus riboflavin the corresponding Z values were 0.00020 (SD = 0.00009) m²/J and 0.00016 m²/J for SARS-CoV-2 and MERS-CoV respectively. However, by comparison SARS-CoV-2 appeared to be more susceptible to UV damage than either SARS-CoV-1 or MERS-CoV when irradiated with UV-C (mean Z = 0.14141 (SD = 0.09045) m²/J) and deep-UV light (mean Z = 0.03684 m²/J).

The calculated Z values for influenza UV-C irradiation experiments undertaken by Heimbuch & Harnish (2019) are presented in Table 5. These experiments, which were carried out using inoculated coupons of respirator material, revealed that in this context the Z values for the various influenza A strains were of the same order of magnitude as those for SARS-CoV-1 and MERS-CoV.

Effective upper-room Z values for aerosolised SARS-CoV-2

A review of the literature revealed that relatively few experimental studies have been performed involving the UV irradiation of aerosolised viruses, with only three undertaken on a coronavirus (Buonanno et al., 2020; Walker & Ko, 2007). A summary of the findings of several key studies are presented in Table 6, which reveals that most viral species appear to be relatively easy to disinfect when suspended in droplets in the air. In particular, aerosolised viruses appear to be more vulnerable to UV damage than when they are suspended in a liquid or on a substrate. For example, for the 24 irradiation experiments involving adenoviruses suspended in liquid, reported by Kowalski (2010), the average Z value was 0.00586 m²/J, which is an order of magnitude less than the values of 0.0546 and 0.0390 m²/J for aerosolised adenoviruses, attributed to Jensen (1964) and Walker & Ko (2007) respectively. Regarding coronaviruses, Walker & Ko (2007) also performed experiments on aerosolised murine (mouse) hepatitis virus (MHV) coronavirus in a single pass test rig. This revealed a Z value of 0.377 ± 0.119 m²/J for this virus. Buonanno et al. (2020) also performed irradiation experiments on aerosolised coronaviruses, but using UV light at 222 nm (far-UV) rather than 254 nm. They found the Z values for human coronavirus 229E and human coronavirus OC43 to be 0.410 m²/J and 0.590 m²/J respectively. Collectively, these Z values are an order of magnitude greater than the values obtained for SARS-CoV-2 in liquid, implying that when aerosolised, coronaviruses in general and SARS-CoV-2 in particular, are much easier to disinfect compared with when they are presented in liquids or on surfaces. Although we are comparing different species of coronavirus here, evidence from Bedell, Buchaklian & Perlman (2016), who irradiated MHV coronavirus and MERS-CoV in Petri dishes, suggests that it is nonetheless valid. They found that 5 min exposed to a UV-C light source resulted in a 2.71 log reduction for the MHV coronavirus, whereas the same exposure resulted in a 5.91 log reduction for MERS-CoV. This suggests that MHV coronavirus is actually more resistant to UV damage than MERS-CoV, and as such, supports Walker & Ko (2007) conclusion that coronaviruses are much easier to inactivate in the air compared with on surfaces and in liquids.

Comparing the computed Z values for UV-C irradiation experiments on the MHV coronavirus conducted in air (0.37700 m²/J (Walker & Ko, 2007)) with those for the SARS-CoV-2 virus in liquid ranging from 0.06280 m²/J (Signify, 2020) to 0.20536 m²/J (Kariwa, Fujii & Takashima, 2006), it would appear that irradiating the coronavirus in liquid requires a UV-C dose that is in the region 1.8–6.0 times higher than that required when the virus is suspended in air. From this we estimated that the value of the adjustment coefficient c_ur would be in a range 0.167–0.545.

Upper-room UVGI computation results

Because no UV irradiation experiments have to date been performed on aerosols containing the SARS-CoV-2 virus, it was necessary when undertaking the feasibility study to make assumptions regarding an appropriate value of Z_ur to use in the upper-room UVGI analysis. With respect to this, because the published mean Z values for the aerosolised coronaviruses were all in the region 0.377–0.590 m²/J, we felt that an assumed Z value in this range would be indicative of how airborne SARS-CoV-2 might behave in a UV-C field. A decision was therefore made to use Walker and Ko’s Z value figure of 0.377 m²/J to evaluate the expected performance of the upper-room UVGI installation, because this was considered a conservative value. In addition, because of the uncertainty associated with this assumed value, we introduced a “factor of safety” into our analysis by also modeling a worst-case scenario in which Z_ur was 0.0377 m²/J.

Table 7 presents the results of the room analysis using these two values for Z_ur, for a range of ventilation rates. From this it can be seen that there is a direct inverse relationship between particle residence time in the UV field, t_uv, and the required irradiation flux, E_r, as predicted by Eq. (8). This means that for any given Z value, the value of E_r will double as the room ventilation rate doubles. The table also reveals that there is a direct inverse relationship between Z_ur and E_r. From the calculated values in this table it can be seen that if Z_ur = 0.377 m²/J, then with an average UV flux of just 10 μW/cm² it should be possible to achieve >90% inactivation of SARS-CoV-2, even at a ventilation rate of 8 AC/h. However, if in reality, Z_ur, is 0.0377 m²/J, then all the calculated fluxes would have to increase by a factor of ten to achieve the same results. Given that accepted guidelines (First et al., 1999b) recommend for a room 2.5 m high, one 30 W (input) UV lamp per 18.58 m² of floor area, which will produce an average flux in the region 50 μW/cm², this means that even under this worst-case scenario it should still be possible to achieve disinfection rates >90% for all but the highest ventilation rates.

When we fixed the UV flux at an average of 50 μW/cm², we found that for Z_ur = 0.377 m²/J the upper-room UVGI installation produced an equivalent air change rate of 108.6 AC/h, whereas if Z_ur = 0.0377 m²/J this fell to 10.9 AC/h. These values were constant and unaffected by the actual room ventilation rate.