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Assessment of the mixing air delivery system ability to protect occupants from the airborne infectious disease transmission using Wells-Riley approach.

Assessment of a mixing air delivery system's ability to protect occupants' from airborne infectious disease transmission using the Wells-Riley equation modified for unsteady heterogenic conditions was performed in this study. Experiments were performed in a field environmental chamber equipped with mixing ventilation, while the cough was simulated using a cough machine. Results show that increase of supply flow rate up to 3 ACH rapidly reduces cough-induced inhalation fraction, but an increase above 6 ACH causes minor changes. When the infectiousness of the index case is relatively low, changes in the supply flow rate will not cause any change in the protective effectiveness of the air delivery system, while for the index case of relatively moderate infectiousness, an increase in supply flow rate up to 6 ACH will improve the protective effectivenes. For the index case of high infectiousness, an increase of supply flow rate will reduce the number of secondary cases for the 8-h exposure period. Maximum protective effectiveness depends only on ability of the system to reduce the exposure, but the index case infectiousness at which this is achieved will depend on the exposure period and exposure reduction.

Introduction

Worldwide emergence of SARS in 2002-2003 and the global influenza pandemic in 2009-2010 brought to our attention the risks and potential impact of worldwide disease spread. Infectious diseases, depending on the infectious agent causing them, can be transmitted via any one of several modes: contact (direct and indirect), droplet, and airborne (CDC 2003). "Airborne transmission refers to the passage of microorganism from a source to a person though aerosols resulting in infection with or without consequent disease" (Li et al. 2007). Factors influencing airborne transmission are ability of the infectious agent to be transmitted by aerosol, source of infectious agents, environmental survival, infectious dose of aerosol transmitted agents, ventilation air patterns (Tang et al. 2006; Cermak and Melikov 2007), operation of the HVAC system (filtration, ultra violet germicidal irradiation [UVGI], recirculation rate), and occupancy of the space (Morawska 2006). Mechanical ventilation and air-conditioning system influence air patterns generated in the space with the air delivery system applied.

Quantitative infection risk assessment of airborne route of transmission of respiratory disease can be performed by the Wells-Riley model and dose-response model (Sze To et al. 2009). The Wells-Riley equation (Riley et al. 1978) was used in several epidemiological studies (Grammaitoni and Nucci 1997; Barnhart et al. 1997; Catanzaro 1982; Fennelly and Nardell 1998; Nardell et al. 1991; Nicas 2000) to quantify the quantum generation rate of the infected person based on available epidemiological data. Nazaroff et al. (1998) and Fisk et al. (2005) included the effects of deposition and control measures to the Wells-Riley equation. Rudnick and Milton (2003) extended the Wells-Riley equation for unsteady-state situations and used C[O.sub.2] as a marker for exhaled breath to calculate the probability of getting infected based on inhaled fraction of air that has been exhaled by the infected occupant. In both studies, assumption of a well-mixed indoor environment was used. Noakes et al. (2006) coupled the Wells-Riley equation with classic epidemic models to include long-term dynamics of infection. Noakes and Sleigh (2009) developed a stochastic Wells-Riley model and coupled it with a multizonal ventilation model to account for proximity of the infector to susceptible and to incorporate mixing in interconnected spaces with each of the zones that were considered as perfectly mixed. Qian et al. (2009) used computational fluid dynamics (CFD) with the Wells-Riley equation to predict concentration levels of pathogens in a hospital ward. Chen et al. (2009) coupled the Wells-Riley approach with viral kinetics and the characteristics of the exhaled bioaerosols in the study of influenza transmission.

[FIGURE 1 OMITTED]

When quantitative infection risk assessment was performed in the previous studies, assumption of the steady-state well-mixed environment was used to determine exposure. This assumption neglects unsteadiness of the cough release (episodic release) and any effect of proximity between the source and potential susceptible occupant to the exposure. In order to replicate unsteadiness of the cough release, experimental measurements of the time-resolved exposure to cough release droplets under different supply flow rates in the single indoor enclosure were performed. The proximity effect of the source was also considered by changing distances among source and target. These measured exposure results were then used to calculate the probability of getting infected and the basic reproductive number in order to evaluate the protective effectiveness of the air delivery system. The aim of this article is to examine the protective effectiveness of a ceiling-mounted mixing air delivery system at various (1) supply flow rates, (2) exposure periods, and (3) index case infectiousness.

Methods

Field environmental chamber (FEC)

An FEC with the floor dimensions shown in Figure 1 and a height of 8.53 ft (2.6 m) was used as the experimental facility in this study. The FEC is supplied by a dedicated air handling unit. A mixing ventilation (MV) system supplied air through six diffusers (perforated panel type) from the ceiling. Six exhaust grills also mounted on the ceiling removed the air from the FEC.

Cough machine

A cough machine was used to simulate the multiphase flow consisting of expiratory droplets suspended in the air generated by a human cough. Human saliva was simulated with a mixture of water (94% of the total volume) and glycerin (6% of the total volume). This method of human saliva simulation has been used in several studies (Chao and Wan 2006; Wan et al. 2007; Chao et al. 2008; Sze To et al. 2009; Pantelic et al. 2009). Characteristics of the cough profile as well as velocities at the cough machine nozzle can be found in Chao et al. (2009).

Aerosol spectrometer

In order to obtain the concentration time profile of the simulated expiratory aerosols, aerosol counting is required. A Grimm 1.108 aerosol spectrometer with 16 size channels (measurable size range 0.98-65.6 [micro]ft [0.3-20 [micro]m]) was used to measure the real-time aerosol concentration in the inhalation zone of a breathing thermal manikin (BTM).

Photo-acoustic spectrometer

An INNOVA 1312 photoacoustic spectrometer multi-gas analyzer was used to determine the air exchange rate (ACH) in the FEC using the tracer decay method by measuring the concentrations of sulphur hexafloride (SF6) over time. A pulse injection of SF6 was performed at the middle of the FEC. Measurements of the decay profile were conducted at two points close to the ceiling (exhaust grills located in the middle of the room at opposite sides in Figure 1) and at the middle of the room at 4.26 ft (1.3 m) from the floor to establish that air was exchanged equally in the whole volume of the room.

BTM

The occupant was simulated using a seated BTM. The BTM comprise 26 body segments that were heated and individually controlled under the "comfort mode." To simulate breathing under light office work, the pulmonary ventilation volume was set at 0.21 [ft.sup.3]/min (6 1/min), with a 10 times per minute breathing cycle comprising 2.5 s of inhalation, a 1.0-s break, 2.5 s ofexhalation, and another 1.0-s break, which was similar to that adopted in Zhu et al. (2005).

Experimental design

The experimental setup was made to simulate an office utilizing an open plan concept. Factors that influence air motion in rooms are velocity at the supply terminal, type of supply terminal, geometry of the room, location of the supply diffuser, location of the extract terminal, obstacles and furniture, and heat load (Etheridge and Sandberg 1996). Air motion through the action of drag force influences cough droplet motion in the environment. Infector and susceptible occupants move through the indoor environment, and due to these movements, relative to each other, cough droplets can be released at several (1) distances, (2) postures, (3) positions around the susceptible occupant, and (4) relative orientations between the infector and susceptible occupants breathing zone. Exposure of the susceptible occupants will be influenced by interaction of cough flow and air distribution system generated air streamlines. This interaction will depend on the abovementioned infector and susceptible factors. In order to take these factors into account, the cough machine nozzle was positioned at four different radii from the manikin: 3.3, 6.6, 9.9 and 13.2 ft (1, 2, 3, and 4 m) (represented as full dots in Figure 1) at heights of 3.77 ft (1.15 m), resembling the sitting posture of infected occupant, or at 4.92 ft (1.5 m), resembling the infected occupant in standing posture. At each radius from the manikin, the cough machine was placed in five different positions relative to the manikin to simulate exposures from the front, side, and back, named, respectively, as lines 1 to 5 in Figure 1. A total of 20 injection points were measured, and due to symmetry, these were deemed to resemble the possible positions of the source (infector) around the susceptible person. Due to the symmetry of the chamber, exposure along lines 1 to 5 were measured, while lines 6, 7, and 8 were taken to be identical to lines 4, 3, and 2, respectively. At each of the measured positions, a cough was injected in eight evenly distributed directions (Figure 1) to simulate the all possible occurences of the cough released by the infector while occupying that particular point in the space. Distances of 3.3 ft (1 m) or greater were chosen based on the the CDC (2003) guidelines for infection disease transmission, which defines large droplet transmission as a mode of transmission at distances of up to 3.3 ft (1 m) between the source and susceptible person and true aerosol transmission occurring at distances larger than 3.3 ft (1 m).

[FIGURE 2 OMITTED]

Number concentration of droplets in the manikin's breathing zone was measured with a Grimm 1.108 spectrometer. The isokinetic probe was positioned 0.05 ft (15 mm) below the manikin's nose and 0.05 ft (15 mm) from the manikin's upper lip. Measurement frequency of the droplet number concentration was 1 s. When the cough is released from the cough machine, the velocity of the droplets decays while droplets are dispersing through the environment. Spatial and velocity droplets distribution depends mainly on the airflow patterns, distance, and direction of the release. Due to dispersion and velocity decay, exposure time will be much longer than release time. An example is given in Figure 2 for two droplet size bins. In order to achieve this measurement frequency, 8 size bins (out of a maximum of 16) were measured simultaneously, and then the same measurement was performed for the other 8 size bins. The average aerosol count over the first 20 s before the time of injection of droplets was taken as the background particle level. This count was subsequently deducted from the droplet number concentration data collected after the cough droplets injection. The measurement period for droplet concentration in the breathing zone was adopted to be 60 s, because it was found that 60 s is a sufficient time period for the concentration level of aerosols to return to the background level in all scenarios studied. Ten repeat measurements were taken for each measurement point, for each direction of the cough, and both heights were explored in this study.

Room air temperature was maintained at 73.4[degrees]F (23[degrees]C) for all experimental runs. Five supply flow rates were measured for MV. Relative humidity in the room was maintained below 70%.

Wells-Riley risk assessment method for unsteady heterogenic environment

Several assumptions were used by Riley et al. (1978) in order to derive the Wells-Riley equation: infectious period of the infector, disease examined is exclusively airborne, infection confers lasting immunity, subclinical cases are neglected, and biological decay of aerosolized microorganism was neglected (perfectly mixed environment, steady-state concentration of airborne infection throughout the exposure period, and neglecting other removal mechanisms except ventilation). Noakes and Sleigh (2009) pointed out a few additional restrictions for application of the Wells-Riley equation: predicts only new cases and that assumption is only valid when incubation period is longer than the time scale of the model, applies only to large population (not taking into account the role of chance effects), and can only be applied for infections that can be modeled with an exponential dose response (Pujol et al. 2009).

The well-mixed assumption is rarely true (Noakes and Sleigh 2009), and it can lead to the underestimation of airborne infectious disease risk (Nicas 1996). In general, steady-state conditions do not apply to indoor particle attributes (Nazaroff and Klepsis 2004). Pathogen-laden expiratory droplets released by breathing, talking, coughing, and sneezing are episodic events; therefore, steady state does not apply when they are considered as sources of indoor pollution. Cough droplets with an initial diameter larger than 80 [micro]m tend to settle quickly onto the floor owing to gravity (Chao and Wan 2006; Chao et al. 2008), and droplets smaller than 80 [micro]m have the ability to evaporate to droplet nuclei size and have a very small response time, which enables them to behave as fluid particles. Neglecting particle depositions on room surfaces is not likely to be valid.

To apply the Wells-Riley equation for the evaluation of an air delivery system as a control measure against airborne infectious disease transmission attributable to cough release, it must be extended to incorporate unsteadiness (cough release) and spatial heterogeneity (source proximity). Intake fraction (iF) for an unsteady heterogenic indoor environment is defined as (Nazaroff 2008)

[iF.sub.ij] = [M.sub.inh]/[M.sub.released] = [[integral].sup.t.sub.0] p(t) x [C.sub.B](t)dt/[M.sub.released] = [bar.p] x [[integral].sup.t.sub.0] [C.sub.B](t)dt/[M.sub.released] (1)

This method of description implicitly takes into account deposition as well as removal by supply flow rate because [C.sub.B] (t) is measured. Production of quanta throughout exposure time is

[M.sub.quanta] = I x [[integral].sup.t.sub.0] q(t)dt = I x [bar.q] x t. (2)

In order to provide a single value that describes the operation of an air delivery system that captures all the factors causing different levels of exposure in the indoor environment, overall averaging was conducted using

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The concept of overall inhalation fraction to characterize a room with a single iF value taking into consideration the impact of different air streamlines, distances, and direction between infector and susceptible occupants is very similar to the concept of a single air exchange value to characterize a whole room.

The Wells-Riley equation for an unsteady-state heterogenic indoor environment is thus

P = 1 - exp [??]-iF x I x [bar.q] x t[??]. (5)

The amount of cough droplets released from the cough machine was used for calculation of [M.sub.released].

Results

Air distribution system assessment with Wells-Riley approach for unsteady imperfectly mixed environments

The process shown in Figure 3a can be used for evaluation of the protective effectiveness of the air delivery system. Results in Figure 3b are calculated using Equation 1 to find the inhalation fraction for every location of cough release, after which these results were applied in Equations 3 and 4 to find the averaged inhalation fraction to characterize a room under a specific flow rate. The probability of getting infected was calculated with Equation 5 for a range of index cases of infectiousness and several possible exposure periods. Results show that the increase of supply flow up to the 6 ACH rate rapidly decreases inhalation fraction, while a further increase of supply flow rate causes much smaller reduction of inhalation fraction. The aerosol sizes used in the experiment were previously used in other studies, and details can be found, for example, in Pantelic et al. (2009). The probability of getting infected and the number of susceptible occupants were then used to calculate the number of secondary cases arising from the presence of a single infector in the environment. The number of secondary cases is also called the basic reproductive number ([R.sub.o]), which was used to characterize the protective effectiveness of the air delivery system.

Impact of the index case infectiousness (quanta generation rate) on the disease transmission patterns for a short exposure period

Results in Figure 4 show the percentage of occupants infected as a function of supply flow rate and index case infectiousness. The percentage of occupants infected can be calculated when the number of secondary cases arising from the single infector ([R.sub.o]) is divided by the total number of susceptible occupants in the room. The total number of occupants in the FEC was taken to be 20 (n = 20), since the average area allocated for an occupant in office space in Singapore is 4 [m.sup.2] (43 [ft.sup.2]).

[FIGURE 3 OMITTED]

Special attention in this study was dedicated to some of the discrete values previously calculated from outbreak cases in several indoor environments. Rudnick and Milton (2003) derived an unsteady-state Wells-Riley equation and used data from the outbreak case investigated by Moser et al. (1979) to calculate the quanta generation rate q = 77 (qph) for influenza. Moser et al. (1979) used a steady-state Wells-Riley equation and calculated q = 128 qph. During an investigation of theoretical limits of protection achievable by ventilation, Nardell et al. (1991) calculated the quanta generation rate for tuberculosis at q = 13 qph from the outbreak data and q = 250 qph from the case reported by Catanzaro (1982). This range of values of q is used in the present analysis.

[FIGURE 4 OMITTED]

When infectiousness of the index case is low (for example, q = 1.25 or q = 13), increase of the air supply flow rate causes minor changes of the percentage of occupants infected (Figure 4). This suggests that when infectiveness of the index case is low and exposure period is short, disease will not propagate through the population occupying that particular indoor enclosure even for low supply flow rate; therefore, increase of air supply flow rate has negligible improvement in protective effectiveness. When infectiveness of the index case is higher (77 qph or higher), increase of air supply flow rate up to 6 ACH causes rapid decrease of the number of people infected. This decrease is more rapid when infectiousness of the index case is higher. These results indicate that supply flow rate has more a important role in occupant protection when the index case has higher infectiveness when the exposure period of the susceptible population is short (t = 8 h). When infectiousness of the index case is 77 qph, a supply flow rate of 6 ACH generates one secondary case. When ACH increases to 12 ACH, there is no increase in the number of secondary cases, which implies that below a certain level of infectiousness of the index case, this increase of air supply flow rate will not have any improvement on disease propagation among the susceptible population in the indoor enclosure. When the index case infectiousness is 250 qph due to the very large infectious load introduced into the environment at 6 ACH, four secondary cases might arise from the single index case, and a further increase of the air supply to 12 ACH reduces the number of secondary cases to three, showing that increase of supply flow rate still makes a positive impact on the transmission dynamics in the environment over a short exposure period.

Impact of the exposure period on disease transmission patterns

Results in Figures 5, 6, and 7 show the percentage of occupants infected in the FEC as a function of supply flow rate and exposure period for a discrete value of the index case infectiousness.

When infectiousness of the index case is low (1.25 qph), a very small difference in the percentage of occupants infected can be observed in Figure 5 for flow rates from 3 to 12 ACH. In the case when air was not supplied to the FEC, for the exposure period beyond 2 weeks, one secondary case can arise. These results show that for the index case with low infectiousness, regardless of the exposure period and air supplied to the FEC, there will be no secondary cases arising. This also suggest that for the low infectiousness of the index case, increasing the air supply flow rate does not make any impact on the protective effectiveness of the occupants even for an exposure period of several weeks. In other words, disease will die off regardless of the ACH supplied to the FEC.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

For the index case of infectiousness of 13 qph for an exposure period of 1 day, there will be no secondary cases even if air is not supplied to the indoor environment, while for the exposure period of 2 days, one new secondary case can arise (Figure 6). These results suggest that for the short exposure period at this level of infectiousness of the index case, increasing supply flow rate is not needed.

When the exposure period is increased to 3 days, when air is not supplied to the environment, two secondary cases can be produced with a single index case, but with an increase of supply flow rate to 3 ACH, the basic reproductive number is reduced below 1.

For the exposure period of 1 week (5 working days) when air was not supplied to the indoor environment, the index case can produce three secondary cases. When supply flow rate is increased to 3 ACH, disease transmission is in an endemic state, which means that one index case produces one secondary case, but a further increase of the supply airflow rate reduces the number of secondary cases below one, suggesting that disease will die off. These results suggest that for an exposure period of 1 week, the supply flow rate deployed in the indoor environment has a large impact on the protective effectiveness of the occupants. Disease dynamics suggest that spread can go from a possible epidemic state, when air was not supplied or supply flow rate was low, to an endemic state for 3 ACH and to die-off stage for supply flow rate beyond 9 ACH.

[FIGURE 7 OMITTED]

When exposure time is increased to 2 weeks (10 working days), increasing the supply flow rate from 0 ACH to 6 ACH reduces the number of secondary cases from six to two. Further increase of air supply flow rate to 9 ACH reduces the basic reproductive number to one, indicating that an endemic state is reached. Further increase of supply flow rate to 12 ACH will not cause the basic reproductive number to reduce below 1, indicating that for 2 weeks exposure period, when infectiousness of the index case is 13 qph, supply flow rate can reduce disease spread from the potentially epidemic to endemic state, but it cannot fully prevent disease transmission in the indoor environment.

For the exposure periods of 3 and 4 weeks, increase of supply flow rate can cause reduction of the secondary cases, but it cannot prevent disease transmission or generate the endemic state.

For the relatively moderate level of infectiousness (77 qph) of the index case, for an exposure period of 1 day (8 h), a supply flow rate of 3 ACH will cause one secondary case; 12 ACH will reduce [R.sub.o] below 1 (Figure 7). If the FEC would not have any supply flow rate, that will lead to a maximum of four secondary disease cases even for an exposure period of 1 day. This emphasizes the importance of operation of the air delivery system, because if failure of the air-conditioning system occurs for one working day while the moderately infectious index case is present in the indoor environment, 8 h of exposure can lead to up to four secondary cases in the susceptible population.

For the exposure time of 2 days (16 h) at the moderate level of infectiousness of the index case, an increase of supply flow rate constantly decreases the number of occupants infected. The number of secondary cases decreases from three at 3 ACH to one at 12 ACH. These results show that disease spread can move from a possible epidemic state to an endemic state with the increase of supply flow rate. They also indicate that under these conditions, airborne transmission in the indoor environment cannot be fully mitigated with MV, even with 12 ACH under these conditions. This trend was also observed in Figure 5 for 13 qph, but for an exposure period of 2 weeks, which suggests that if index case infectiousness attains acertain value for a given exposure period, MV faces a lot of challenges in providing protection for the susceptible occupants in the indoor environment.

If the exposure period is increased beyond 2 days, results suggest that increase of the supply flow rate can only reduce the number of secondary cases, but disease will continue to spread through the susceptible population. When the exposure period is very large (e.g., 4 weeks) while index case infectiousness is 77 qph, an increase of supply flow rate from 3 to 12 ACH reduces 4 secondary cases from 15 to 11. These results show that when the index case has a moderate level of infectiousness while the exposure period is long, MV does not have the ability to prevent disease spread even at 12 ACH and can only reduce the number of cases.

Infections prevented for various index case infectiousness and supply flow rates

Results shown in Figures 8 to 11 show the number of infections prevented as a function of index case infectiousness and supply flow rate. The number of infections prevented represents the difference between the number of secondary cases arising when 1 ACH of supply flow rate was supplied to the environment and the number of secondary cases generated at the particular supply flow rate used in the FEC. In the analysis of the results, it was assumed that air supplied to the FEC does not contain any airborne pathogens and that the only source of potentially infectious airborne pathogens is cough release from the one infected occupant. When air is exhausted from the FEC, it was assumed that it is exposed to in-duct (or in AHU) ultraviolet germicidial irradiation and further downstream to filtration, which will inactivate or remove all the pathogens from the air released by the index case. When this set of technologies is applied, air patterns generated in the room are responsible for reduction of exposure, and there is no distinguishable difference between ventilation and recirculation air. In the operation of a normal air delivery system, the function of ventilation can be separated from the total air supply, because recirculated air can contain airborne pathogens from the previous cough releases and can re-introduce them into the environment. In the operation of a normal air delivery system, only ventilation air can perform dilution of the airborne pathogens; therefore, results presented can be used to understand performance of a 100% outdoor air supply system or system that has capability to disinfect and filter out airborne pathogens.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

For an exposure period of 1 day (8 h), the number of infections prevented increases with the increase of index case infectiousness, because for a short exposure period, the higher the infectious load in the indoor environment, the greater the ability of the MV system to prevent infection for the range of quanta explored (Figure 8). With the increase of supply flow rate, the number of infectious cases prevented will be increased for the given quanta generation rate. The difference among supply flow rates increases with an increase of index case infectiousness.

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

When the exposure period is increased to 3 days (24 h), the MV system has a peak number of infections prevented for a particular index case infectiousness (Figure 9). This shows that the supply flow rate system exhibits optimal protective performance (saturation point) at certain conditions. Optimal protective performance of the MV will depend on (1) the exposure period, (2) infectiousness of the index case, and (3) supply flow rate used (Figures 9, 10, and 11). For a given exposure period and supply flow rate of air, optimal protective performance will be achieved for a certain index case infectiousness. This index case infectiousness is called the critical quanta generation rate ([q.sub.critical]). Critical infectiousness can be calculated with Equation 6. If the infectiousness of the index case is increased above this critical value, dilution achieved with supply flow rate will not be sufficient to remove the infectious load from the indoor environment; hence, the number of infections prevented will be reduced. The number of infections prevented will be reduced with the more noteworthy increase of index case infectiousness beyond critical value (Figures 9, 10, and 11):

[q.sub.critical] = ln([iF.sub.1]/[iF.sub.1])/([iF.sub.1] - [iF.sub.x]) x t. (6)

For a given exposure period, an increase of the air supply flow rate of the system allows [q.sub.critical] to increase; for example, for an exposure period of 3 days, [q.sub.critical] = 175 qph for a supply flow rate of 3 ACH, but for 12 ACH, [q.sub.critical] = 220 qph. This suggests that for a given exposure period, [q.sub.critical] will depend on the dilution characteristics of the air supply system achieved at various supply flow rates.

Equation 6 also suggests that if exposure period is increased, [q.sub.critical] will decrease for a particular supply flow rate. This can be observed from Figures 10 and 11, where for the exposure period of 2 weeks for a supply flow rate of 3 ACH, [q.sub.critical] = 50 qph, and for a supply flow rate of 12 ACH, [q.sub.critical] = 68; for the exposure period of 4 weeks (20 working days), for a supply flow rate of 3 ACH, [q.sub.critical] = 22 qph, and for a supply flow rate of 12 ACH, [q.sub.critical] = 29. This reduction of the differences among [q.sub.critical] for the different air supply flow rates is due to the increase of the denominator value (exposure period increase while inhalation fraction values are unchanged).

The maximum number of infections prevented does not change with exposure period. In some cases due to short exposure period (1 day in Figure 9), the maximum value of the infections prevented are not shown for the infectious quanta per hour generation used in this study. The maximum number of infections prevented depends on (1) number of susceptible occupants and (2) relationship between inhalation fraction for a given supply flow rate and inhalation fraction when indoor environment had an air supply of I ACH, as shown in Equation 7:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Discussion

The results in Figure 4 show that during day exposure to a single moderately infectious index case (77 qph), in the susceptible population of 19 occupants, could generate four secondary cases when air was not delivered to the indoor environment. For the same environmental conditions and number of susceptible occupants, a highly infectious index case (250 qph) can generate ten secondary cases. If 3 ACH were supplied while 77 qph were released by a the infected case, disease transmission would reach the endemic state, where only one secondary case would arise, while at 250 qph release, five secondary cases could potentially emerge. These results show that having no air delivery generates a significantly higher risk of infection for the occupants. Failure of the air delivery system may occur for one working day in the office buildings, and if this takes place at the same time when an infected occupant with moderate or high infectiousness is present in the indoor environment, epidemic outbreak can take place in that office environment. This possibility brings into focus the reliability and maintainability of the air supply system as one of the most important system characteristics. This issue is especially important for systems that utilize complex control mechanisms, which, if not properly maintained and regularly checked, can cause system failure, possibly causing infection outbreak as previously demonstrated. Even air delivery systems with high potential to provide protection for the occupants from airborne infection disease transmission, like desktop personalized ventilation (Pantelic et al. 2009), need to be designed for reliability, because short exposure during a failure period to a sufficiently infectious source can cause an outbreak episode.

Changes of the MV supply flow rates can have a range of impacts on the airborne disease transmission dynamics in the indoor environment. Conditions that are determinants of the MV protective effectiveness are (1) infectiousness of the index case, (2) exposure period for susceptible occupants, and (3) capability to reduce exposure. As shown in the previous section, low infectiousness in the index case will not cause changes in disease propagation, regardless of the air delivery system operation. On the other hand, for a moderate level of index case infectiousness, changes in the air supply and exposure period significantly altered the outcome of disease propagation in the susceptible population. With the increase of index case infectiousness, air supply variations have a large effect even for a short exposure period.

Equation 7, for the maximum number of cases prevented ([DELTA][R.sub.o max]) with a particular air delivery system, reveals that [DELTA][R.sub.o max] can only be increased if [iF.sub.x]. is increased. Figure 3b shows that [iF.sub.x] can be decreased with the increase of supply flow rate but efficiently only up to 6 ACH, while a further supply flow rate increase causes far less reduction of [iF.sub.x]. When HEPA filters are used in the air handling units, such an increase of supply flow rate causes a very large energy penalty for the system, because power consumption of the system will rise with the third power of velocity. This implies that the set of technologies should be used for infection control rather than relying only on the dilution characteristics of the mixing air delivery system. Alternative air delivery options should be considered that enable delivery of more fresh air into the breathing zone, for example, the desktop personalized ventilation system, which is able to reduce exposure (Pantelic et al. 2009) in room air filtration, or perhaps introducing local air ionization for inactivation of viruses and bacterias.

Distribution of occupants during office hours, together with the spatial distribution of pollutants present in the indoor air, represents a key determinant of occupant exposure. Yang et al. (2004) demonstrated that when personalized ventilation caused accumulation of pollutants in some parts of the indoor environment, depending on the spatial distribution of occupants, total exposure of the occupants can be higher compared to the usage of MV. When an infection source is present in the space (infected occupant who releases potentially infectious droplets via cough), spatial and temporal distribution of the occupants around the source will determine their exposure and levels of risk via airborne transmission route. Nobe et al. (2002) measured occupied density (OD), which represents the ratio of time spent inside the workstation and the total time spent at the workplace, and showed that it is a function of the job performed (0.47 for clerical work). This result indicates chance of infection based on the amount of time person spends seated at his/her workstation and standing outside the workstation is approximately equal. In the case of airborne infection transmission, that means that occupants can be exposed to the release from a sitting and standing infector's posture with almost equal probability, assuming that healthy and infected person behave similarly. This assumption is used in the present study, but it should be pointed out that OD is function of the job type. Another assumption made in the present study is the equal exposure contribution of cough releases from an infector to the susceptible for distances from 1 m (3.28 f) to 4 m (13.12 ft). Infector (source) and susceptible occupants move through the indoor environment in a similar manner, while cough release is an episodic event that causes exposure for a short period of time; hence, due to the uncertainties and unsteadiness of the phenomena, it is practical to assume equal contribution of several distances among infector and susceptible occupants for the purpose of air delivery system analysis.

Limitations

The absence of more heat sources (apart from the BTM), the static environment (without movement of occupants), the type of the ceiling-mounted supply diffuser used and their distribution with respect to exhaust grills, and the absence of office furniture in the experimental setup represent limitations of the present study.

Conclusion

This study has analyzed the influence of the supply flow rate, index case infectiousness, and exposure period on protective effectiveness of MV against the airborne mode of infectious disease transmission. The major conclusions follow.

* An increase of supply flow rate up to 3 ACH rapidly reduces inhalation fraction, but an increase above 6 ACH results in minor improvement in protection against cough-induced inhalation fraction.

* When the infectiousness of the index case is relatively low (1.25 qph or 13 qph), changes of the supply flow rate leads to negligible improvements in the protective effectiveness of the air delivery system, while for the relatively moderate index case infectiousness (77 qph), an increase of supply flow rate up to 6 ACH leads to observable improvement in the protective effectiveness; however, for an index case of high infectiousness (250 qph), an increase of supply flow rate will constantly decrease the number of secondary cases for the short exposure time (t = 8 h).

* For low index case infectiousness (1.25 qph) for an exposure period of up to 4 weeks, changes of supply flow rate will not affect protective effectiveness of the MV. When index case infectiousness is 13 qph, a short exposure period (up to 2 days or 16 h) will make no impact on protective effectiveness, but for the longer exposure period (up to 2 weeks), an increase of the supply flow rate will cause significant changes of protective effectiveness (reduction from possible epidemic state to die-off state of disease transmission). Results also show that this behavior is present for the 77-qph index case release but for an exposure period of 1 or 2 days. For a very large exposure period (3 or 4 weeks) and a release of 13 qph, an increase of the supply flow rate can only reduce number of secondary cases. A similar pattern can be observed if the index case releases 77 qph, when the exposure period must be beyond 2 days.

* An air delivery system has the maximum protective effectiveness (number of cases prevented by a particular airflow rate). Maximum protective effectiveness depends only on the ability of the system to reduce the exposure, but the index case infectiousness ([q.sub.critical]) at which it will be achieved depends on the exposure period and exposure reduction. With the increase of exposure period, [q.sub.critical] will be reduced. An above [q.sub.critical] MV system reduces its protective effectiveness.
Nomenclature

[B.sub.ij] = weighted coefficient for contribution of
 a particular point of cough release
[C.sub.B](t) = concentration of pathogen-laden
 droplets in the breathing zone,
 [m.sup.3](liquid)/[m.sup.3](air)
 [[ft.sup.3](liquid)/[ft.sup.3](air)]
i = distance between infector and receptor
I = number of infectors (I = 1 in this study)
iF = averaged inhalation intake fraction
[iF.sub.1] = inhalation intake fraction when air is not
 supplied to the FEC
[iF.sub.ij] = inhalation intake fraction for every
 cough release position
[iF.sub.x] = inhalation intake fraction for a particular
 supply flow rate
j = position of the infector along the circumference
 along each circle
[M.sub.inh] = mass of the inhaled cough released
 droplets, kg (lb)
[M.sub.released] = total mass of cough droplets released by
 infected occupant, kg (lb)
n - 1 = number of susceptible occupants in the
 FEC when single infector is present
P = probability of getting infected
p(t) = pulmonary ventilation rate, [m.sup.3]/h
 ([ft.sup.3]/h)
[bar.q] = average quanta generation rate throughout
 exposure period, quanta/h
[q.sub.critical] = critical index case quanta generation
 rate at which maximum number of infections
 is prevented
q(t) = quanta generation rate, quanta/h
[R.sub.o] = basic reproductive number
t = exposure period, h
w' = weighted coefficient for potential exposure
 of direct cough from sitting posture
w'' = weighted coefficient for potential exposure
 of sitting posture release compared
 to standing posture
w''' = weighted coefficient for potential exposure
 of direct cough from standing
 posture
[[alpha].sub.i] = area contribution for contribution of different
 floor areas at different distances
 among source and susceptible
[DELTA]
 [R.sub.o max] = maximum number of infections prevented


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Jovan Pantelic * and Kwok Wai Tham

Department of Building, School of Design and Environment, National University of Singapore, 4 Architecture Drive, 117566, Singapore

* Corresponding author e-mail: bdgjp@nus.edu.sg

Received March 14, 2011; accepted November 9, 2011

Jovan Pantelie is PhD. Kwok Wai Tham, PhD, is Associate Professor.

DOI: 10.1080/10789669.2012.647230
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