Selected references ASHRAE. Ashrae handbook. Atlanta: 2005.

1. Input-output Correlation Sensitivity Analysis for Environmental Standards for Bacillus Anthracis Spores Tao Hong1,Patrick Gurian1, Nicholas Dudley Ward2 1Department of Civil, Architectural and Environmental Engineering, Drexel University 2Pattle Delamore Partners, New Zealand B. Dose-response model Background Bacillus anthracis is an aerobic, Gram-positive, non-motile, spore-forming bacterial species which is the causative agent of anthrax, a potentially fatal bacterial infection. Envelops containing Bacillus anthracis spores were mailed to news media companies and government officials separately in 2001 (Fig. 1), which caused the death of 5 people and cost hundreds of millions of dollars to clean the contaminated buildings. Fig.1. Letters used in 2001 anthrax attacks (FBI) Since human health risk from biological agents is associated with aerosol exposures, it is suggested that concentrations found on surfaces may be used to infer future or past aerosol exposures. When these concentrations indicate that aerosol exposures exceed specified values, they would trigger response actions, such as remediation (to avoid future risks) or prophylactic antibiotics (to mitigate risks of past exposure). II. Prospective scenario In the prospective scenario, the risk is related to the concentration of Bacillus anthacis on the tracked floor under the assumption that spores from other surfaces are not reaerosolized. The inhaled dose is determined by integrating equation (6) with Cair expressed as mass of Bacillus anthracis spores in the aerosol compartment divided by volume of the room, when times goes infinity: (7) Where Γ is termed future risk coefficient. Results Numerical values of model input parameters are provide in Tables 2. Fig. 3 and Fig. 4 shows the relationship between accumulative risk of mortality and time for different particle sizes for retrospective scenario and prospective scenario, respectively. For detail please refer to Hong (2009). Table 2. Model inputs Monte Carlo simulation Monte Carlo simulation is fulfilled based on the ranges of inputs from Table 2, and uniform distribution is assumed between boundaries. Simulation results are presented in Fig. 5, Fig 6 and Table 3. Table 1 Surface concentration-risk equation Previous studies indicate that exponential function (Eq. 1) provides a favorable fit for Bacillus anthracis spores with particle size smaller than 5μM, and beta-Poisson function (Eq. 2) fits well for spores with diameters larger than 5 µM (Bartrand, Weir et al. 2008; Teunis and Havelaar 2002; Haas 2002): risk =1- exp(-r dose) (1) (2) where risk is the probability of infection, dose is the average number of inhaled spores, r is the probability that a single organism will survive to initiate infection, and α, β are parameters of beta distribution. When the product of r and dose is relatively small, a first-order Taylor series can be used to approximate equation (3) and (4) as: risk =r dose (3) (4) N50 is median infection dose. Since the initial conditions for retrospective and prospective risk are different, we consider these two different scenarios separately in the following. C. Release scenarios Two scenarios on individuals exposure to Bacillus anthracis are taken into account. One scenario is termed retrospective risk and the other prospective risk. For the retrospective scenario, an individual was assumed to be exposed to Bacillus anthracis spores which were released in the air of a room instantaneously, while for the prospective scenario, it was assumed that Bacillus anthracis has been deposited on a tracked surface, which corresponds to a post-event scenario following settling. Mathematically this corresponds to changing the initial conditions to a release on the tracked floor and using the same model that had been as previously described for the retrospective scenario. Retrospective risk estimates would inform measures for mitigating prior exposures, such as administering prophylactic antibiotics, while prospective risk estimates would inform decisions for mitigating future exposures, such as environmental remediation and re-occupancy standards for contaminated buildings. D. Linking risk with surface concentration I. Retrospective scenario Concentrations in several of the environmental compartments are linear functions of the integral of past air concentrations. As the dose is also a function of the integrated air concentration, it is possible to obtain relationships between environmental concentrations and retrospective human health risk in which time is not an explicit variable. The concentration of Bacillus anthacis on the untracked floor is the integrated number of spores deposited over time (ta-tb), divided by the area of the untracked floor, Auf: (5) Assuming that the occupants of the room have experienced the exposure from the beginning (a health protective assumption as discussed above), which can be expressed mathematically as t1= ta= 0 and t2= tb, one can combine equation (5) and equation (6) to link the dose with the concentration on untracked horizontal surfaces: (6) (7) The deposition rate onto the untracked floor for Bacillus anthacis (λuf) is a function of deposition area, volume of the room, and corresponding deposition velocity (νuf with the unit m/s) (Thatcher and Layton 1995). Thus equation (7) can be rewritten as: (8) At low doses, equation (8) can be combined with equation (1), the Taylor series approximation of an exponential dose-response function, to link the probability of mortality with the concentration of Bacillus anthacis on the untracked floor (Eq. 9). Table 1 includes surface concentrations-risk equations for other surfaces. (9) Table 3 Correlation between human risk and other input parameters It is generally accepted that the U.S. remains vulnerable to the risk of suffering another bioterrorist attack. However, the US lacks guidelines for a quick response to such attacks which will allow responders to estimate who were exposed during the attack and what level of risk these exposed individuals face; also the U.S. does not have standards for what is the safe concentration of Bacillus anthracis for reoccupation of a building after decontamination. Fig. 5. Monte Carlo results for retrospective scenario Fig. 6. Monte Carlo results for Prospective scenario • Model Introduction • A. Fate and transport model • Fig. 2. Schematic of model • The model was built based on a simple occupied office suite with a heating ventilation and air conditioning (HVAC) system as in Fig. 2. The office was divided into 7 internal compartments: air, tracked floor, untracked floor, walls, ceiling, HVAC, and in the nasal passages of an occupant of the office. • The following system of linear first order ordinary differential equations was obtained based on the mass balance relationships among different compartments in the office suite: • Mce(t) is the Bacillus anthacis on the ceiling at time t. • Mn(t) is the Bacillus anthacis in people’s nasal passages at time t. • Mair, Mtf, Mutf, Mw, Mf, Mec, Mce and Mn are all given in units of spores (number of organisms). • Q is the discharge from the air compartment (computed from ACH assumptions). Units are [m3] • λtf, λutf, λw and λce are the deposition rates onto the tracked surface, the untracked surface and the floors, • walls and ceiling respectively. Units are [T-1] • µ2 is the resuspension rate from the untracked surface into the air compartment. Units are [T-1] • p is the fraction of air recirculated into the building by the HVAC system. • e is the efficiency of the filter at removing particles. • en is the efficiency of the nasal passages at removing particles. • I is the rate of the occupant. Units are [m3/hour]. • V is the volume of model the room Units are [m3]. • Conclusion • For prospective and retrospective scenarios, the risk of mortality can be linked with the concentration of Bacillus anthracis on surfaces and HVAC filters; • Accurately measuring these levels presents an analytical challenge. Detecting well-aerosolized B. anthracis (diameter of 1 µM) will be particularly problematic; • Uncertainties in dose response contribute the most to overall uncertainty in standards; uncertainties in deposition velocities are significant sources of uncertainty for the larger particle sizes, while HVAC recirculation rate contributes substantial uncertainty to the 1 µM particles; • This analysis does not account for decay over time, recovery, or discounting of future risk. Selected references ASHRAE. Ashrae handbook. Atlanta: 2005. Bartrand, T. A., M. H. Weir, et al. Dose-response models for inhalation of bacillus anthracis spores: Interspecies comparisons. Risk Analysis, 2008; 28 4: 1115-1124. Brachman, P.S., 1966. “Industrial Inhalation Anthrax,” Bacteriological Reviews, 30(3):646-656. Druett, H.A., 1953. “Studies on Respiratory Infection. I. The Influence of Particle Size on Respiratory Infection with Anthrax Spores,” Journal of Hygiene, 51:359-371. EPA. Exposure factors handbook. Washington, DC : Exposure Assessment Group, Office of Health and Environmental Assessment, U.S. Environmental Protection Agency, 1997. Hass, C.N. 2002. “On the Risk of Mortality to Primates Exposed to Anthrax Spores,” Risk Analysis, 2(2):1218-21. Tao Hong (2009). Estimating Risk of Exposure to Bacillus Anthracis based on Environmental Concentration. Civil, Architectural and Environmental Engineering. Philadelphia, Drexel. M.S. thesis. Kowalski, W. J. Immune building system technology. New York: McGraw-Hill, 2003. Lai, A. C. K. and W. W. Nazaroff. Modeling indoor particle deposition from turbulent flow onto smooth surfaces. Journal of Aerosol Science, 2000; 31 4: 463-476. Landahl, H. On the removal of air-borne droplets by the human respiratory tract: Ii. The nasal passages. Bulletin of Mathematical Biology, 1950; 12 2: 161-169. Mitchell-Blackwood, J. and P. L. Gurian (2008a). An evaluation of the risk threshold for prophylaxis and treatment after an anthrax release. Mitchell-Blackwood, J., P. L. Gurian, et al. (2008b). A hierarchical model for probabilistic dose-response assessment of bacillus anthracis. NRC. Reopening public facilities after a biological attack: A decision-making framework. 2005. Teunis, P. F. M. and A. H. Havelaar. Risk assessment for protozoan parasites. International Biodeterioration & Biodegradation, 2002; 50 3-4: 185-193. Thatcher, T. L. and D. W. Layton. Deposition, resuspension, and penetration of particles within a residence. Atmospheric Environment, 1995; 29 13: 1487-1497. Sextro, R. G., D. M. Lorenzetti, et al. Modeling the spread of anthrax in buildings. 2002; Schneider, T., J. Kildeso, et al. A two compartment model for determining the contribution of sources, surface deposition and resuspension to air and surface dust concentration levels in occupied rooms. Building and Environment, 1999; 34 5: 583-595. • Mair(t) is the Bacillus anthacis in the air • compartment at time t. • Mtf(t) is the Bacillus anthacis on the tracked • surface of the floor at time t. • Mutf(t) is the Bacillus anthacis on the untracked • surface of the floor at time t. • Mw(t) is the Bacillus anthacis on the walls at time t. • Mf(t) is the Bacillus anthacis on the filter at time t. • Mec(t) is the Bacillus anthacis in the external • compartment at time t. Fig. 3. Accumulative risk of mortality and time for different particle sizes (retrospective scenario, 1000 spores released) Acknowledge This project was funded through the CAMRA Center of Excellence by a grant from the Department of Homeland Security, Science and Technology Directorate, Office of University Programs and the Environmental Protection Agency. The authors also would like to acknowledge Professor Agami Reddy’s valuable input on HVAC system parameters. Fig. 4. Accumulative risk of mortality and time for different particle sizes (Prospective scenario, 1000 spores released)