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Airborne disease infection risk modeling Lin, Chu 2012

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Airborne Disease Infection Risk Modeling  by Chu Lin  B.A.Sc., The University of British Columbia, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  September 2012  © Chu Lin, 2012  ii  Abstract A mathematical model which estimates spatial infection risk as a function of pulmonary rate and deposition region has been developed based on the does-response model. It is specifically designed for enclosed space with consideration of pathogen bio-properties, such as viability and infectivity. Firstly, eleven cases of Tuberculosis (TB) outbreaks in aircraft are studied to develop the optimal parameters set. It is then used to perform model validation and investigation of sample inpatient room spatial infection risk. Secondly, infection risk for eleven TB outbreaks are compared with modeling and Wells- Riley estimations. As a result, modeling results are within the calculated range of Wells- Riley prediction. To determine the importance of viability and ventilation rate regarding HVAC system design for health facilities, infection risks are calculated at different viability and ventilation rates. Based on the observation, ventilation rate or particle concentration in the space dominate the infection risk distribution, except when viability decays extreme rapidly. Thirdly, the spatial infection risk is investigated for TB in a typical 60 m3 inpatient room with displacement and well-mixed ventilation systems. Two room settings, a nurse standing close to the patient’s bed versus a visitor standing far away from the bed, and two coughing directions, horizontal versus vertical, are studied. The results show that for coughing horizontally, when the nurse stands beside the patient's bed, his/her breathing zone is the highest risk zone for displacement ventilation. Under displacement ventilation, the infection risk is lower when visitor stands away from the bed compared to stand close to the bed if the visitor is the only person present in the room besides the patient. The infection risk of the iii  breathing zones in the two cases with horizontal coughing are both higher than 25%. However, when a patient coughs vertically, the displacement ventilation significantly reduces the infection risk. With 24 hours exposure, the infection risk for the nurse and the visitor are both less than 5%.   iv  Table of contents Abstract ..................................................................................................................................... ii Table of contents ...................................................................................................................... iv List of tables ............................................................................................................................. vi List of figures .......................................................................................................................... vii Acknowledgements .................................................................................................................. ix 1 Introduction ....................................................................................................................... 1 1.1 From epidemic outbreaks to evidence of airborne transmission ................................ 1 1.2 Infection risk models .................................................................................................. 7 1.3 Thesis scope and objectives ..................................................................................... 10 2 Infection risk modeling ................................................................................................... 12 2.1 Dose-response model ............................................................................................... 12 2.1.1 Wells-Riley equation ........................................................................................ 13 2.1.2 Spatial infection risk model .............................................................................. 15 2.1.3 Computation Fluid Dynamics (CFD) data processing ...................................... 24 2.2 Spatial risk model for TB ......................................................................................... 25 2.2.1 Ranges of parameters ........................................................................................ 25 2.2.2 Optimal parameter values ................................................................................. 26 2.2.3 Results and discussion for aircraft cases ........................................................... 34 2.3 Summary of model development and validation ...................................................... 38 v  3 Results and discussion .................................................................................................... 40 3.1 Infection risk for an inpatient room under DV and mixing system ......................... 42 3.1.1 Coughing horizontally ...................................................................................... 43 3.1.2 Coughing vertically ........................................................................................... 49 3.2 Ventilation rate versus viability ............................................................................... 53 3.3 Summary of infection simulations ........................................................................... 58 4 Conclusions and future work .......................................................................................... 60 4.1 Conclusions .............................................................................................................. 60 4.2 Model strength and limitation .................................................................................. 61 4.3 Future work and recommendation ............................................................................ 62 Bibliography ........................................................................................................................... 63 Appendix A: MATLAB code ................................................................................................. 71 Appendix B: Airplane cabin space calculation ....................................................................... 81 Appendix C: TB outbreak cases ............................................................................................. 83 Appendix D: Parameter sensitivity investigation ................................................................... 93 Appendix E: Influenza outbreak cases .................................................................................... 94 Appendix F: Influenza infection risk modeling and viability study ....................................... 97 Appendix G: Cough frequency studies ................................................................................. 102 Appendix H: Particle distribution ......................................................................................... 104  vi  List of tables Table 2-1 Particle aerodynamic diameter size bin ranges ...................................................... 19 Table 2-2 Infection risk for actual outbreaks .......................................................................... 28 Table 2-3 Summary of parameter uncertainty level ............................................................... 31 Table 2-4 Parameter IF ........................................................................................................... 32 Table 2-5 Cases summary for optimal parameter value selection .......................................... 33 Table 2-6 Model inputs of upper and lower bound for TB outbreaks .................................... 35 Table 2-7 Actual outbreaks vs. modeling results & actual outbreaks vs. Wells-Riley ........... 37 Table 3-1 Model input for DV horizontal cough .................................................................... 43 Table 3-2 Model input for different ventilation rate case ....................................................... 54    vii  List of figures Figure 1-1 TB global trend of incidence, prevalence and morality. ......................................... 4 Figure 1-2 Global estimated incidence rates in 2010 ................................................................ 5 Figure 1-3 Spatial infection risk for ward 8A during 2003 SARS epidemics in Hong Kong hospital ...................................................................................................................................... 9 Figure 2-1 Particle number distribution of a cough based on Chao's distribution .................. 19 Figure 2-2 Particle volume distribution of a cough ................................................................ 20 Figure 2-3 Fractional deposition for human respiratory system. ............................................ 21 Figure 2-4 Total deposition fraction vs particlediameter.   ..................................................... 22 Figure 2-5 Overall deposition and deposition for three regions. ............................................ 23 Figure 2-6 Infection visk for actual TB outbreaks .................................................................. 29 Figure 2-7 Actual outbreak infection risk compared with upper and lower bound of modeling results ...................................................................................................................................... 35 Figure 2-8 Actual infection risk vs modeling results and Wells-Riley equation results ........ 36 Figure 3-1 Schematic for two room settings ........................................................................... 40 Figure 3-2 Schematic for 3 zones. .......................................................................................... 41 Figure 3-3 Schematic for 9 zones ........................................................................................... 41 Figure 3-4 Infection risk for one zone when coughing horizontally ...................................... 44 Figure 3-5 Infection risk for 3 zones with 24 hours exposure when coughing horizontally .. 46 Figure 3-6 Infection risk for 9 zones with 24 hours exposure when coughing horizontally .. 48 Figure 3-7 Infection risk for one zone when coughing vertically ........................................... 50 Figure 3-8 Infection risk for 3 zones with 24 hours exposure when coughing vertically ...... 52 Figure 3-9 Infection risk for 9 zones with 24 hours exposure when coughing vertically ...... 53 viii  Figure 3-10 Infection risk for different air change rate with mixing ventilation system and 24 hours exposure ........................................................................................................................ 55 Figure 3-11 Infection risk at different viability under ACH=1, 4 and 8 for the well-mixed room ........................................................................................................................................ 56 Figure 3-12 Infection risk for coughing horizontally (nurse stands beside the bed) for DV and well-mixed cases ..................................................................................................................... 57 Figure 3-13 Infection risk for coughing horizontally (visitor stands away the bed) for DV and well-mixed cases ..................................................................................................................... 58   ix  Acknowledgements First of all, I would like to express my enduring gratitude to my supervisor Dr. Steven N. Rogak for his invaluable guidance and exceptional patience in making this thesis possible. I would like to also thank Dr. Sheldon I. Green and Dr. Karen H. Bartlett for their continuous guidance and support during my research. Many thanks go to my colleague Amir A. Aliabadi for his helpful suggestions and support. I also would like to thank Paul Marmion for providing significant advice and guidance to my thesis from the industrial perspective. Furthermore, I would like to thank NSERC and Stantec for their financial support.  Many thanks to my colleagues, James Montgomery, Bronson Patychuk, Ehsan Faghani, Hugo Tjong, KeigoKarakama and Yunfei Zhang for their help and support. I also would like to thank HaiyaPeng, Cleo Wong, Ryan Chiew and Brian Har for reading my thesis.  Special thanks to my parents and friends for their endless encouragement and continuous support throughout these years.      1  1 Introduction Infection risk is defined as the probability that a susceptible host will contract an infection from a known infected individual over a defined exposure time. To illustrate the importance of infection risk research, this chapter reviews three epidemics: Tuberculosis (TB), Severe Acute Respiratory Syndrome (SARS) and Influenza A (H1N1). Some historical evidence is given to prove the existence of airborne transmission, which has been a controversial topic for decades. Further, this chapter discusses the pros and cons of infection risk models, which can be illustrated by reviewing two infection risk models: one with emphasis on predicting spatial infection risk distribution, and one focusing on bio-properties of the pathogen. As both factors are essential when assessing the infection risk, a model which takes into account both risk factors is desired. Keeping this goal in mind, the project scope and objectives will be detailed at the end of this chapter. 1.1 From epidemic outbreaks to evidence of airborne transmission Theoretical epidemiology shows that a communicable disease transmission would take place only when three indispensable factors are present: a susceptible host, corresponding routes and at least one infectious dose of pathogen. Transmission routes are usually categorized into three major groups: (1) physical contact, (2) droplet and airborne transmission and (3) fecal-oral transmission. (1) Physical contact. Direct physical contact requires extremely close contact between the pathogen source and the susceptible host, e.g. touching an infected wound or hand contacting membrane of eyes and/or nose. Indirect physical contact requires touching of contaminated surfaces or inanimate objects, such as handling used medical equipment,  2  clothing, bedding or soil. These actions would be sufficient for diseases transmission (Nicas & Sun, 2006). (2) Fecal-oral transmission. This type of transmission results from drinking or eating contaminated water and/or  food. (3) Droplets and airborne transmission. Droplets transmission refers to the infection caused by interaction with larger coughing/talking/sneezing droplets that carry infective pathogen. Since these droplets are driven by gravity or inertia (Zhu, et al., 2006) and settle out of air rapidly (Xie, et al., 2009), this type of transmission is limited to close proximity. Airborne transmission results from small droplets from coughing/talking/ sneezing. For smaller droplets, after experiencing evaporation and condensation in approximately 0.8s after a coughing event (Morawska, et al., 2009), they become airborne. As pathogen carrier, airborne is driven by air current and can remain suspended in the air for a long time. This feature significantly expands the area and distance that the pathogen carried by the airborne can spread. The research in this thesis focuses solely on airborne transmission. Airborne transmission has been a controversial subject since the concept was brought onto the table during the 1950s (Riley, et al., 1962). There are two primary reasons for the controversy: (1) Airborne as a disease transmission route was not recognized six decades ago, whereas other transmission routes and pathogen viability have been well known in studies for a much longer time span(Riley, 1974). (2)  The definition of airborne transmission is not standardized in terms of particle diameter. Even today, based on differing perspectives and methodologies when quantifying airborne transmission, there is no universal agreement for the benchmark of the particle  3  diameter that distinguishes between droplets from airborne particles. While some authors define <100 µm particles to be airborne (Duguid, 1946), others believe <50 µm is the defined range (Zhu, et al., 2006). In order to explain the historical development of the airborne transmission concept, three diseases are reviewed to illustrate its role in actual epidemic state and the necessity of airborne infection risk modeling studies.  Tuberculosis  (TB) TB is an infectious lung disease caused by bacillus Mycobacterium tuberculosis. Although in general, most exposed people are asymptomatic, the risk for people with the human immunodeficiency virus (HIV) is significantly greater (World Health Organization (WHO), 2011). Although the global incidence1 of TB has been showing a slight decay since 1990, except for HIV-positive TB, WHO estimated there were still approximate 8.8 million TB incidence cases globally in 2010. Among those, 12-14% were HIV-positive as shown in Figure 1-1. Geographically, the incidence rate is significantly higher for certain areas or countries. e.g. Southern Africa, Myanmar and Cambodia. Figure 1-2.   1 Incidence rate measures the occurrence of new cases within a specific study period among initial population exposed to the risk. For example, if 30 new cases developed over three years and initially there was 2000 people, the incidence rate is: 30/(2x3)=5  per 1000 people per year.   4   Figure 1-1 TB global trend of incidence, prevalence and morality. (WHO, 2011)The left figure: the top green line indicates the global estimated incidence rate of TB including HIV-positive TB, the lower red line indicates the estimated global incidence rate of HIV-positive TB; the middle figure indicated the global prevalence of TB and estimated trend up to 2015; the right figure indicates the global prevalence of TB and estimated trend up to 2015  Shown in Figure 1-1, the global prevalence2 and mortality3rate of TB has been declining since 1990. The black dashed lines indicate the Stop TB Partnership targets of a 50% decrease of prevalence and mortality rate by 2015, which compared to the rate in 1990. According to WHO’s estimation in 2010, about 1.7 million people died of TB in 2010, among those, 0.4 million were HIV-positive (WHO, 2010).   2 Prevalence measures how much of a disease or condition occurs in a population at the time the study was performed. For example: of total examined population 6139 at one time, 519 currently had the condition. The prevalence is 519/6139=0.085 or 8.5%. (Roe & Doll, 2000) 3 Mortality rate measures the number of death in a period per unit of population. For instance: among 100,000 people, 60 died because of one disease from 2008 to 2009. The mortality rate is 30 per 100,000 per year.  5   Figure 1-2 Global estimated incidence rates in 2010 (WHO, 2011) Due to TB’s high infectivity and mortality rate (without treatment), it has been a global health problem for over 100 years (WHO, 2011). However, the concept of airborne transmission of TB was first brought to attention in the mid-1950s by Wells, and demonstrated by a guinea pig experimental study a decade later. This study took place at Veterans Hospital in Baltimore and used guinea pigs as the susceptible host. In this experiment, approximately 120 guinea pigs were placed on the roof of a penthouse where TB patients resided and were considered as pathogen source (Riley, et al., 1962). After 4 years of exposure, 134 guinea pigs contracted TB (Riley, 1974). This experimental study is the earliest evidence of airborne disease transmission. In the following years, several different environmental set-ups, e.g. homes and hospitals, were used to carry out the studies regarding airborne transmission as a possible transmission route (Riley, 1974; Bates & Nardell, 1995). The airborne drops from the respiratory secretion of TB patients was soon identified as viable pathogen carriers which were small enough to go through the ventilation ducts and flow with air currents.  6  Severe Acute Respiratory Syndrome (SARS) The outbreak of SARS in 2002-2003 gained global attention by its extremely high prevalence and mortality rate. From November 2002, the emergence of the first identified SARS case, to May 2003, 28 countries reported a cumulative 7761 SARS probable cases with 623 deaths. Among those, China mainland reported 5209 cases and 282 deaths. (WHO, 2003). During the outbreak, SARS, a highly infectious corona-virus (Lipsitch, et al., 2003),was believed to be spreading from person to person by contaminated droplets which required close contact with an infected individual (Noakes & Sleigh, 2009). Meanwhile, there was some evidence showing that the newly infected individuals were not sufficiently close to the known infected beings, and thus suggests that transmission occurred by means of the air flow route (Noakes & Sleigh, 2009; Li, et al., 2005; Qian, et al., 2009). The airborne transmission, therefore, was concluded as one of the SARS infection route.  Influenza A (H1N1) The 2009 influenza pandemic was caused by a novel Influenza A (H1N1) virus. It is also known as Swine Flu and Influenza A pandemic (H1N1) 2009 virus. From April 2009, the first emergence of the H1N1 case in Mexico, to July 2010, 214 countries, territories or communities reported a cumulative laboratory confirmed 134,503 cases with 816 deaths associated with H1N1 influenza virus (Han, et al., 2009). Although for some specific cases studies showed that there was not enough evidence to conclude that airborne transmission was the main route for H1N1 virus (Han, et al., 2009), more retrospective cohort studies showed that people who were infected or had positive influenza-like illness (ILI) test results did not have direct contact or close communication with known infected individuals (Foxwell,et al., 2011; Baker, et al., 2010).  7  Other diseases with significant airborne transmission Common diseases that spread through airborne transmission also include measles, smallpox, chicken pox, etc. Although there are vaccines available to prevent fatal outbreaks, the high possibility of contraction is still a threat for people who work or stay at high occupancy density places. e.g. health care facilities, public buses, trains or air flights. In order to ameliorate the understanding of infection risk, both mathematical and experimental models are built to simulate and predict infection risk. The following section will review infection risk models to narrow down this project's objectives.  1.2 Infection risk models The purpose of building an infection risk model is to help researchers understand the retrospective outbreaks efficiently and help designers to optimize design of health facilities designs, such as ventilation system. As a result, energy efficiency and airborne disease control could be achieved simultaneously.  The infection risk model remained undiscovered until the 1950s, when Wells first proposed the concept of infection quantum (Wells, 1955). Over 20 years later, Riley implemented Well's concept into an equation by applying the best fitting method and using an actual set of outbreak data. Since then, the famous Wells-Riley equation was formed and is still widely used as the base for infection risk modeling. Due to airborne particles being driven by air currents, simulation regarding air paths will help people gain a better perspective of possible routes through which the disease can spread. An infection risk model can be built based on tracking particle movement. Previously, several  8  experimental studies had been carried out to examine dispersion characteristics and spatial distribution of expiratory particles in an enclosed space (Zhang, et al., 2009; Sze To, et. al, 2009).e.g. hospital ward or aircraft cabin. Tracer gas, as the surrogate of particles emitting from respiratory activities, e.g. coughing or sneezing, is one of the major techniques used to develop this type of model (Zhang, et al., 2007; Wang, et al., 2006). While the experimental tests provide more reliable data, the numerical studies could offer more flexibility in simulating different environmental conditions (Zhao, et al., 2004; Gupta, Lin, & Chen, 2011; Zhang & Chen, 2007). While computational results agreed with experimental observations (Zhang & Chen, 2006), it is a time consuming process; therefore it is not recommended for assessing particles distribution in complicated environments with long exposure time (Zhang & Chen, 2006).e.g. an aircraft cabin with full load passengers and long flight hours.  Regarding spatial infection risk assessment, Qian proposed a spatial risk distribution model to investigate a nosocomial outbreak in Hong Kong during the 2003 SARS epidemics (Qian, et al., 2009). This model integrated Wells-Riley equation into Computational Fluid Dynamics (CFD) and simply neglected viability and infectivity change. The overall pathogen decay rate was expressed by a linear relationship. In this paper, the quanta generation at different filter efficiencies, 100%, 50% and 0% were estimated based on one session, 40 minutes exposure. According to the author, the infection risk using this set of quanta generation overestimated adjacent and distance cubicles. Figure 1-3 shows that the spatial infection risk distribution. The distribution was presented at heights of 1.6 m (considered as breathing zone) and 1.05 m.  9   Figure 1-3 Spatial infection risk for ward 8A during 2003 SARS epidemics in Hong Kong hospital (A) at the height of 1.6 m with 40 minutes exposure (B) at the height of 1.05 m with 160 minutes exposure; (1) filter efficiency =100%, q=78 (quanta/min); (2) filter efficiency = 50%, q=68 (quanta/min); (3) filter efficiency = 0%, q=41 (quanta/min)(Qian, et al., 2009) While Qian built the model with emphasis on spatial distribution of infection risk, Nicas upgraded Wells-Riley equation by implementing bio-properties of pathogen and four types of viable pathogen particle removal mechanisms. The bio-properties include pathogen concentration in respiratory fluid and emission rate. The removal mechanisms are mechanical ventilation, particle settling, air disinfection methods and die-off (Nicas, et al., 2005). Despite the lack of spatial infection risk distribution, Nicas's model took into account size distribution of particles and pathogen bio-properties upgrading Wells-Riley equation in different aspects.  10  The importance of understanding airborne disease transmission is growing and is essential in predicting and preventing future outbreaks of diseases. Therefore, a model that could predict spatial airborne infection risk which takes into account the bio-properties of pathogens is desired.  1.3 Thesis scope and objectives The project in this thesis is sponsored by Stantec and NSERC. The main objective is to simulate and investigate the infection risk in an inpatient room. The results can be used to help building designer optimize ventilation systems which reduce airborne transmission infection risk.  According to literature review, no spatial infection risk model has yet been developed to investigate and compare the importance of pathogen viability and ventilation rate setup regarding airborne disease control. A mathematical model therefore will be built for this purpose while implementing bio-properties and generation rate of pathogen, pulmonary rate, deposition fraction of susceptible people and ventilation systems. e.g. infectivity, viability and cough frequency. To further narrow down the scope of this project, the model developed in this thesis is designed for a closed space with limited movement of subjects. e.g. an inpatient room. The major assumptions are that the subjects are at fixed locations during the entire exposure time, and there is only one post infected person initially. To study the reliability of modeling outputs, Wells-Riley equation and actual outbreaks are used as comparison reference.  In Chapter 3, the model is then applied to a specific inpatient room to determine the spatial distribution of infection risk. Two sets of scenarios are studied. The first set is the location of the subjects: a nurse standing beside the patient's bed and a visitor standing further away from the  11  bed. The second set is the coughing direction: coughing horizontally and coughing vertically. The modeling results will be further compared with Wells-Riley equation. As a result, the thesis recommends whether the bio-properties should be neglected and whether ventilation rate plays a more profound role in the infection risk modeling.  Chapter 4 will introduce a brief set of conclusions and recommendations for future work.      12  2 Infection risk modeling This chapter introduces the mathematical infection risk model developed for airborne diseases prediction through the explanation of the equations and parameters involved in detail. To achieve a good confidence level for result from the model, TB outbreaks, which took place on commercial flights, are used as the scenarios to determine the optimal parameter set. The modeling results will be compared with actual outbreaks and Wells-Riley estimations. At the end, an investigation of the variance for infection risks due to different viability and ventilation rate is carried out. The result is then used to determine whether it is necessary to take viability into account while design HVAC systems for health facilities.  2.1 Dose-response model The model developed here is based on the dose-response model. In particular, the infection risk is calculated from the total dose of the infectious pathogen deposited into the respiratory system of susceptible people over the exposure time. In other words, the possibility for susceptible people to become infected by a certain type of pathogen, after exposure time t, depends on the total number of infectious pathogens deposited into his/her respiratory system. The principle equation is as follows: ܲ(ݐ) = 1 − exp (−ܦ(ݐ))                                                 (1) Where ܲ(ݐ) is the probability of infection risk at time t, (%); ܦ(ݐ) is the accumulative dose deposits into the susceptible respiratory system from time 0 to time t.   13  2.1.1 Wells-Riley equation The Wells-Riley equation is a particular case of a dose-response model. It was derived from experimental data/actual outbreak statistics. The Wells-Riley equation has been widely used as a tool to predict infection risk. It considers the number of infectors, pulmonary ventilation rate of susceptible people, the quanta generation rate for the pathogen and the ventilation rate. The Wells-Riley equation (Riley, et al., 1978): ܲ(ݐ) = ஼ௌ = 1 − exp (− ூ௤௣௧ ொ )                                                      (2) Where ܲ(ݐ) is the probability of infection risk at time t, (%); ܥ is the number of infection cases; ܵ is the number of susceptible persons; ܫ  is the number of infectors; ݌  is the pulmonary ventilation rate, (m3/s); ݍ is the quanta generation rate, (quanta/s); ݐ is the exposure time, (s); ܳ is ventilation rate, (m/s). There are two main assumptions for the Wells-Riley equation. • Particles are evenly distributed in space, which means the infection risk predicted by this equation is uniform within the space; • The equation neglects viability and infectivity of the pathogen quanta. By noticing that the possibility to get infected for susceptible people at a certain area was significantly higher (Qian, et al., 2009), a model capable of predicting specific spatial infection risk is desired. Each parameter involved in the Wells-Riley equation is described below.  Infector In the Wells-Riley equation, the number of infectors indicates the number of initial pathogen carriers. Considering that this number might vary with exposure time, a mathematical model,  14  based on this equation, has been built by setting the infector as one of the variables (Liao, et al., 2005); therefore it can predict the long term infection risk for a large population more accurately.  Quanta generation rate In epidemiology, a “quantum” (or “unit”) describes the minimum dose of pathogen which is infectious and capable of reproducing. The dose also is known as the unit. Quanta generation rate here defines how quickly the unit dose of the pathogen is generated. This value is determined by fitting the model to experimental data. The quanta generation rate is unique for each disease and also depends on different environment condition. e.g. For most TB cases, the TB quanta generation rate can be assumed as to be between 1.25 to 60 quanta/hour (Noakes & Sleigh, 2009).  Pulmonary ventilation rate Pulmonary ventilation rate, also known as respiration rate, describes the frequency and volume of air exchange between human lungs and ambient surrounding. The unit is liter per minute. The pulmonary rate varies with age. For newborns and young children, the pulmonary rate is normally higher than it is for adults. The pulmonary pattern also depends on health condition and activities that a person is performing. For instance, compared to a person at rest, the tidal volume for people who are sleeping is usually smaller. (Douglas, et al., 1982)  Ventilation rate Ventilation rate is the measurement of air exchange rate between the defined space and outside. The unit for this parameter is air change per hour (ACH). Normally, this rate is determined by  15  combining a mechanical system and the hybrid. e.g. an activated displacement ventilation with door opening.  2.1.2 Spatial infection risk model The spatial infection risk model developed in this thesis is based on a model established by Sze To in 2009 (Sze To & Chao, 2010), Equation (3). P(ݔ, ݐ௢) = 1 − exp ቀ− ∑ ௝ܴܨ௝ ௦݂ݐ௢ܿ௢݌௠௝ୀଵ ׬ ܦ(ݔ, ݐ)௝ܵ(ݐ)݀ݐ௧೚଴ ቁ                       (3) Where P is infection risk at location x at time to; ݉ is the total number of size bins; ݆ is the jth size bin; ܴ is infectivity of pathogen; ܨ is deposition fraction (%); ݂ is cough frequency (s/times); to is time exposure (s); ܿ௢is pathogen concentration in mucus (#/m3); ݌ is the pulmonary rate of susceptible host (m3/s); ܦ(ݔ, ݐ) is particle volume density at location x at time t (m3/m3); ܵ(ݐ)is viability of pathogen. Compared to Wells-Riley, Sze To’s model calculates the accumulative dose deposited into the respiratory system of susceptible people using a different approach, which assumes coughing/sneezing/talking are the only events that generate particles carrying pathogen. From the size of the particles that can deposit into susceptible people, the corresponding volume of these particles can be estimated based on the particle distribution profile for a single coughing/sneezing/talking event. By knowing the frequency of the event occurrence, exposure time, susceptible person's breathing pattern, particle dilution rate, pathogen concentration and decay rate, the accumulative dose at any time t can be calculated. The infection risk is determined from this accumulative dose. The model developed in this thesis follows the same logic as Sze To’s model. The following section will explain the methodology for modified model development systematically.  16  Two ventilation systems are examined in this thesis: well-mixed ventilation and displacement ventilation. For well-mixed ventilation, the total volume of fluid in a single cough emission can be calculated as: ௣ܸ_௢ = ∑ ௢ܰ௝ݒ௝ ௌ௜௭௘ ஻௜௡௦௝ୀଵ ܨ௝                                                    (4) Where ௣ܸ_௢ is the total volume of  particles which could get deposited into respiratory system if the air is inhaled (m3); ௢ܰ௝ is the total number of particles which generated by one cough event for Size Bin j at time step 0 (#); ݒ௝ is the volume of a single particle in Size Bin ݆ (m3); ܨ is the same as described in Equation (3). In particular, ݒ௝is calculated as follows: ݒ௝ = ସଷ ߨ( ஽೘೔೙ೕା஽೘ೌೣೕ ସ )ଷ                                                       (5) Where ܦ௠௜௡௝ is the lower bound of the particle diameter in Size Bin j (m); ܦ௠௔௫௝ is the upper bound of the particle diameter in Size Bin j (m). The total dose, ܦ௢ , deposited into susceptible respiratory system for any single cough during the exposure time is expressed as: ܦ௢ ቀݐ − ே೔௙ ቁ = ׬ ௏೛_೚ ௏ ܿܵ(ݐ)ܴ݌݁ ିೂೇ௧݀ݐ௧଴                                          (6) Where Ni is the ith cough during the time exposure; ݁ି ೂ ೇ௧ is the particle removal rate from the system, in which ܳ is the ventilation rate (m3/hour) and ܸ is the spatial volume of the room (m3); ݐ is the time exposure (s), ݐ > ே೔௙  . In Equation (6), the particle removal rate is described as ݁ିೂೇ௧. This is also considered in the purge equation, Equation (7), while the initial concentration, ܥ௣_௢, is 100%. ܥ௣_೟(ݐ) = ܥ௣_௢݁ି ೂ ೇ௧                                                        (7)  17  Where ܥ௣_೟ is the concentration of the property at time t. For displacement ventilation, at time t, the total remaining volume, ௣ܸ_௧, of any single cough emission is calculated as: ௣ܸ_௧ = ∑ ௝ܰ(ݐ)ݒ௝ ௌ௜௭௘ ஻௜௡௦௝ୀଵ ܨ௝                                                (8) Where ௝ܰ(ݐ) is the remaining number of particles for a single cough in size bin j at time t. ܦ௢ is calculated as: ܦ௢ ቀݐ − ே೔௙ ቁ = ׬ ܿ௢ܵ(ݐ)ܴ݌ ଵ ௏ ௣ܸ_௧݀ݐ ௧ ଴                                          (9) Where all parameters are defined the same as discussed before. For the total dose, ܦ(ݐ), deposited into the respiratory system up to time t, which is also known as the accumulative dose of multiple coughs at time t, the same equation can be applied for both types of ventilation. The equation is expressed as follows: ܦ(ݐ) = ∑ ܦ௢ ቀݐ − ே೔௙ ቁ ே೎೚ೠ೒೓ ே೔ୀ଴                                                 (10) Where ௖ܰ௢௨௚௛ is the total number of coughs during the entire time exposure. With knowing the accumulative dose up to time t, the infection risk can be calculated by applying Equation (1). With information of each particle's diameter and location at any time t, the spatial infection risk is determined by first dividing the entire space into desired zones and then assuming all the particles within each zone are evenly distributed. Treating each zone as an individual space, the equation developed above can be used to calculate the infection risk. In this paper, this model is named Zone Model. As the Zone Model can vary with different investigation focus, it has advantage in saving time and simplifying analysis process. For instance, when the research focuses on the breathing zone for visitors in an inpatient room, a two-zone condition can be  18  defined to model this case: Zone 1 is the breathing zone and Zone 2 is the rest of the room. Increasing the number of zones or reducing the volume of each zone will help to locate more specific spatial risk in the room. By using this method, the infection risk distribution in the room can be studied and examined more thoroughly.  In addition to parameters involved in the Wells-Riley, Equation (2), particle size distribution, deposition fraction, pulmonary rate of susceptible host, pathogen viability and infectivity also play important roles in the spatial infection risk model. Excepting infectivity, all these parameters are size dependent. In the following paragraphs, the logic behind the model development and parameters value/range selections will be explained by introducing the concept and relationship between parameters.  Particle distribution for coughing, sneezing and talking Several studies have investigated particle distribution for a single cough event. While applying different techniques and methodologies to quantify the total number of particle and estimate the initial particle size, there are variations among the reported values. The particle distribution used in this paper is based on Chao's study (Chao, et al., 2009). According to Chao, the particle distribution captured at distance of 10mm from the mouth is more accurate than Duguid (Duguid, 1946) and Loudon and Roberts (Loudon & Roberts , 1967) studies. However, due to the sampling method Chao used, the total volume of expiratory fluid is not measured. Taking Duguid, Loudon and Roberts (LR) and Zhu's (Zhu, 2004) experimental results for the total volume and then appling Chao's distribution, the normalized particle number and volume distribution are plotted in Figure 2-1 and Figue 2-2 respectively. The particle size bin ranges,  19  Table 2-1, are adopted from Chao (Chao, et al., 2009).  The CFD data, which will be used as displacement ventilation reference, is plotted in the same figure for later comparison purposes. Table 2-1 Particle aerodynamic diameter size bin ranges  Size bin 1 Size bin 2 Size bin 3 Size bin 4 Aerodynamic diameter range  (µm) 1-4.5 4.5-8 8-16 16-24   Figure 2-1 Particle number distribution of a cough based on Chao's distribution LR, Duguid, Zhu and Zhao’s original number of particle distribution are provided by Chao (Chao, et al., 2009).CFD data is provided by Amir A. Aliabadi (please refer to Section 2.1.3 for more details)  0 1000 2000 3000 4000 5000 6000 1 10 100 1000 dN /d ln Dp  (# /m 3 ) Diameter (µm) Number Distribution Based on Chao's distribution LR (1967) Duguid (1946) Zhu (2006) Chao (2009) CFD data  20   Figure 2-2 Particle volume distribution of a cough LR, Duguid, Zhu and Zhao’s particle original number distribution are provided by Chao (Chao, et al., 2009).CFD data is provided by Amir A. Aliabadi (please refer to Appendix H for original particle distribution)   Deposition fraction of respiratory system and pulmonary rate The particle size range that will be studied specifically for this model can be narrowed down to the ones that can deposit in the human respiratory system. Based on data from the International Commission of Radiological Protection, Harkema predicted the particle deposition fraction for nasopharyngeal, tracheobronchial, and alveolar region during nasal breathing (Oberdorster, et al., 2005). As shown in the following figure, for the nasal airway, referring to the upper/blue section in the top right figure, particles with diameter <0.01µm and higher than approximately 20 µm have larger fractional deposition. The fractional deposition fraction for tracheobronchial and 1.E-16 1.E-15 1.E-14 1.E-13 1.E-12 1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1.00 10.00 100.00 1000.00 dV /d ln Dp  (m 3 /m 3 ) Diameter (µm) Volume Distribution Based on Chao's Distriubtion LR (1967) Duguid (1946) Zhu (2006) Chao (2009) CFD data  21  alveolar regions, referring green and red section in the graph in the right middle and right bottom figures, have the similar tendencies: both having peak deposition at around 0.005 to 0.01µm and up to 10 to 20 µm. This sectional deposition fraction for the human respiratory system lays out a simple and clear picture for further investigation of particle deposition. According to research, certain diseases have higher concentration in particles at specific diameters. For example, studies show that particles with approximately 5µm diameter have higher TB pathogen concentration, and these particles are more viable and infective. This fractional deposition information thus can be used as input information for infection risk modeling development.  Figure 2-3 Fractional deposition for human respiratory system. Drawing courtesy of J. Harkema.(Oberdorster, et al., 2005) Based on the above discussion, the overall particle deposition in the respiratory system is less than 100µm; and for tracheobronchial and alveolar region it should be less than 10 to 20 µm. This information is useful for narrowing down the particle study range for different diseases. Particle deposition fraction also depends on the tidal volume and speed. To investigate the deposition for extra thoracic region, tracheobronchial region, alveolar region and total deposition  22  for different diameter particles, Choi drew the following figures based on published experimental data.   Figure 2-4 Total deposition fraction vs particle diameter.  The empty symbol drawings are based on Heyder's experimental data. The solid symbol drawings are based on Kim and Jaques's experimental data. (Kim & Hu, 1998; Jaques & Kim, 2000). Drawing courtesy of J. Choi.  (Heyder, et al., 1986)   23   Figure 2-5 Overall deposition and deposition for three regions. Total (solid line); extrathoracic (dashed line); tracheobronchial (dash-dotted line); alveolar deposition (dash-dot-dotted line). Top figure: ௧ܸ = 500 ݈݉ ܽ݊݀ ܳ = 250݈݉/ݏ ; middle figure: ௧ܸ = 1000 ݈݉ ܽ݊݀ ܳ = 250݈݉/ݏ; bottom figure: ௧ܸ = 1000 ݈݉ ܽ݊݀ ܳ = 500݈݉/ݏ. The original experimental data are based on several studies. (Chan & Lippmann, 1980; Heyder, et al., 1986; Kim & Hu, 1998; Stahlhofen, et al., 1989)Drawing courtesy of J. Choi. By knowing the deposition region of a disease and pulmonary pattern, the deposition fraction can be estimated using above figure.    24  Infectivity Infectivity measures the capability of a living disease agent to enter, survive in and reproduce in a susceptible host.  Viability Viability measures the survivability of the pathogen. Viability is highly dependent on surrounding environmental conditions, for instance, temperature and humidity. When the pathogen is still viable, it is not necessarily infective; however, for infective pathogen, it must be viable.  2.1.3 Computation Fluid Dynamics (CFD) data processing A set of data, which simulates cough particles distribution over 440 seconds in a 3m x 4m x 5m inpatient room with displacement ventilation at 4 ACH, is available to use as reference for this model. This data is obtained using CFD software. It recorded particle information, three dimension coordinates, velocity, diameter, etc., with 10s interval. Particle distribution is shown in Figure 2-1 and Figure 2-2. The distribution is re-weighted, using Equation (11), for each size bin based on the literature reported distribution. ܰ௠,௝(ݐ) = ܰ௠,௢,௝ ே಴ಷವ,ೕ(௧)ே಴ಷವ,೚,ೕ                                                        (11) Where Nm,j is number of particles at time t (#) in size bin j which is based on CFD data and will be used in the model; Nm,o,j  is number of particles in size bin j based on literature reported distributions, such as: Duguid's (Duguid, 1946) or Chao's  (Chao, et al., 2009) as shown in Figure 2-1, at time 0, (#); NCFD,j  is number of particles in size bin j based on CFD data at time t, (#); NCFD,o,j  is number of particles in size bin j initially based on CFD data, (#). After knowing the  25  number of particles at each time step, accumulative dose can be determined using Equations (8), (9) and (10). The infection risk can be calculated by applying Equation (1).  2.2 Spatial risk model for TB To further test and develop the model, TB is used as a sample disease due to its prevalence and high infectivity. TB aircraft cabin outbreaks are selected as references scenario to determine the optimal parameters of the model. At the end of this section, the modeling results will be compared to actual outbreaks' and Wells-Riley equation's results.  2.2.1 Ranges of parameters Understanding the possible ranges and types for each parameter is essential in selecting the most reasonable and optimal set of parameters as model input. The following section will introduce the parameters for TB infection model.  Viability Although TB is a well-known disease due to its high infection and death rate, so far there is no study reporting a certain value or standard to quantify the viability of TB. Based on research conducted on this topic, the survivability of the TB pathogen highly depends on environmental conditions. TB pathogen can live for hours, days, even months and longer. Thus, since the exposure in this study is the first 24 hours, the viability for TB is assumed as one.    26  Infectivity Due to the high infectious rate of TB, infectivity is assumed to be 1 for most current infection risk modeling. By treating infectivity as a variable, the model input value can be changed as new information become available.  For simplicity, the infectivity is assumed as 1 for TB, which means once one infectious pathogen gets deposited into a susceptible respiratory system, the susceptible people will get infected.  Particle deposition and size range According to published sources, pathogens of TB have higher fractional deposition in the alveolar region. As shown in Figure 2-6, the dash-dot-dotted line, particles deposited in the alveolar region are approximately <10 µm. Particle size here refers to the diameter of particles that have finished aerosolization. Applying Nicas theory (Nicas, et al., 2005) that the particle will shrink down to one half of the original diameter after aerosolization, for orignial particle distributions, the diameter range that will be focused in this thesis is about  <20 µm.  2.2.2 Optimal parameter values As discussed in the previous sections, there are wide ranges or different types of values available for each parameter. In order to closely compare the infection risk to the actual outbreaks, parameter value selection is very important. This section introduces the process applied while establishing infection risk model for TB. For comparison and testing purpose, actual TB outbreak cases are collected and studied for their infection risk. Recalling that the scope of this study is to investigate the infection risk in an inpatient room, selecting the actual outbreak cases with common environmental and physical  27  conditions would aid in increasing the confidence level for the designed model. Therefore, train, airplane and hospital wards are the primary investigated locations for case searching. For a train trip or a flight, during the travelling time, the space within the cabin is considered as closed space with mechanical ventilation system. With limited movement of subjects during the trip, the particles carrying pathogens are assumed to be solely driven by ventilation force. All these features mentioned are comparable with the environmental condition in an inpatient room. So far, nineteen TB cases are collected to accomplish this task. Please refer to Appendix C for case details. Some studies pointed out that a flight shorter than two hours lack sufficient evidence to show that airborne is one pathway for TB transmission (Moore, et al., 1996). Traditionally, the area less than five rows away from the infector/TB pathogen carrier are the high-risk zones compared to other locations within the cabin. However, based on the cases collected for this section, several people get infected during a short flight, less than two hours; people also showed positive skin test even when they sat more than five rows away from the patient. Thus, in this study, all outbreaks, with short travelling time, are taken into consideration. The actual outbreak case infection risk is calculated using the following equation. ௔ܲ௖௧௨௔௟ = ே೔೙೑೐೎೟೐೏ே೟೚೟ೌ೗ ೛೚೛ೠ೗ೌ೟೔೚೙ × 100%                                                 (12) Where ௔ܲ௖௧௨௔௟ indicates the infection risk for actual outbreaks;  ௜ܰ௡௙௘௖௧௘ௗ is the total number of people who get infected during the event, e.g. one flight; ௧ܰ௢௧௔௟ ௣௢௣௨௟௔௧௜௢௡ is the total population involved in the event, e.g. passengers and crews on the flight. Among nineteen TB cases, eleven of them took place on the airplane without interchanging trip with bus or train. Thus, the following calculation will take these eleven cases for analysis.  28  Understanding the process of determining if people are infected during the flight will be useful to quantify the uncertainty of the actual infection risk. After confirmation of the presence of a TB pathogen carrier on the plane after the flight, a survey was sent to all passengers and crews. Among those who replied and did a skin test, people who showed positive results were considered as infected. Because not everyone replied to the survey, there is a variance for the recorded infected number. Taking TB Case 12 as an example, the total population on the plane was 343. Among those, 79 did a skin test, and results showed that eight of them were infected. Assuming no one in the rest of the population, people did not reply the survey, were infected, the infection risk was 2.33% by using Equation (12). If there was the same or higher percentage of people in the rest of the population who got infected, the infection risk would be >10.13%. In the following calculation, only the lower end, e.g. 2.33% for TB Case 12, will be used for future calculation assuming that it's common sense for all people having TB symptoms to reply to the survey. Table 2-2 Infection risk for actual outbreaks Case1 Exposure time (hour) # of infected Total population Infection Risk Ref. 3 14 16 225 7% (Wang, 2000) 6 1.25 5 120 4% (Moore, et al., 1996) 10 8.63 15 257 6% (CDC, 1995) 12 9 8 343 2% (McFarland, et al., 1993) 13 0.5 1 22 5% (CDC, 1995) 14 8.5 32 219 15% (Miller, et al., 1993) 15 18 14 661 2% (CDC, 1995) 16 8 7 298 2% (Kenyon, et al., 1996) 17 1.75 4 104 4% (Kenyon, et al., 1996) 18 2 3 109 3% (Kenyon, et al., 1996) 19 8.75 15 249 6% (Kenyon, et al., 1996) Note: 1. the Case number corresponds to TB outbreak cases listed in Appendix.  29  Considering the model developed here is an exponential decay function and theoretically with zero possibility of infection risk at time zero, the best fitting line should past through the (0,0) point. Therefore, additional point (0,0) is added to 11 actual points from the outbreak to calculate the best fitting line.  Figure 2-6 Infection risk for actual TB outbreaks As shown above, the linear relationship between the infection risk and exposure can be expressed as ܫ݂݊݁ܿݐ݅݋݊ ܴ݅ݏ݇ = 0.0047ݐ.  To output the most reasonable estimations, the modeling results are therefore expected to be as close as possible to this line.  Sensitivity of parameter Based on previous discussion, the selection of input value for each individual parameter is not unique while making the estimated infection risk as close as possible to the best fitting line. For example, the model would produce the same result for both situations: y = 0.0047x 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 0.160 0 5 10 15 20 In fe ct io n Ri sk  (% ) Exposure Time (hours) Linear (Actual outbreaks)  30  (1) reducing the cough frequency while increasing corresponding breath rate of susceptible people; (2) holding both parameter values as they are. Furthermore, for some of the parameters, there is a significant variance for the actual values. e.g. the cough frequency and pathogen concentration in the cough fluid. These two parameters are highly case-dependent. Thus, to produce the most reasonable infection risk based on available information, it is essential to determine the optimal combination of parameters' value. The strategy applied here is to investigate the parameter uncertainty level first. The uncertainty level is determined based on its independency, which means how many other factors could have influence on this parameter. For parameters with lower level of uncertainty, the values for them will be set as input first. With parameters with higher and same level of uncertainty level, sensitivity analysis for them will be carried out. Parameters with least sensitivity will be considered first. In fact, sensitivity analysis was performed on four parameters, including cough frequency, particle distribution, pulmonary rate and pathogen concentration.  The sensitivity, in this thesis also called Impact Factor (IF), is calculated using the following equation. ܫܨ௉ = ோ௜௦௞೘ೌೣ,೛ିோ௜௦௞೘೔೙,೛ோ௜௦௞೘೔೙,೛                                                       (13) Where IFp is the impact factor of parameter p, p is cough frequency or particle distribution, etc; Riskmax,p is the maximum probability of infection risk for parameter p when fixing other parameters; Riskmin,p the minimum probability of infection risk for parameter p when fixing other parameters. The summary of parameter uncertainty level is tabulated as follow, along with the sensitivity table for four parameters. Sixteen sample cases are used to determine IF for these four parameters and detailed in Appendix D. Although ventilation rate has a low uncertainty level, IF  31  is also calculated. The purpose of this is to gain a better understanding of the overall impact on the infection risk between ventilation rate and other parameters. Table 2-3 Summary of parameter uncertainty level Parameter available range (based on literature review) uncertainty level target deposition region alveolar  Low (Could be determined once the disease, which the model designed for, is selected, if the information is available.) deposition fraction ~<10µm Low (Once the deposition region is determined, the fraction can be read from figure presented in Section 2.2.2) exposure hours 0 ~24 hours (the model is designed to predict the infection risk in 24 hours) Very low (Can set an number between 0~24) ventilation rate  Case dependent (e.g. for Boeing 767, the standard operation rate is 1052 m3/hour) 1 Very low room size Case dependent (e.g. for Boeing 767, the main cabin is estimated at 420.5 m3) Very low number of infector 1 (the model is designed as when the initial number of infector is 1) Low viability 1 Medium (For TB, the literature reports that the pathogen can survive for days and even months. Thus, in this paper, the viability for TB within 24 hours is assumed as 1 over the entire exposure time. infectivity 1 High (Based on literature, TB is highly infective airborne disease. The infectivity is assumed as 1.) cough frequency 3 times/hour 2 12 times/hour3 High (Cough frequency is highly case dependent. It varies with patients conditions and so on. )    (continued in the next page)  32  Parameter available range (based on literature review) uncertainty level particle distribution Duguid (1946); Loudon and Roberts (1967); Chao(2009); High (Due to different equipment, technologies and methodologies are applied to quantify the number of  particles in different size bins, the results could be varied. )6 pulmonary rate Case dependent (e.g. typical assumptions: 250 or 500 ml/s)4 High pathogen concentration 8.4 x 106  (ml-1) 5  Very high (pathogen concentration in the cough fluid basically is an uncertain number. The range from 105 ~ 109 (ml-1) is used to preliminary calculation in this paper. ) Notes: 1. (Wang, et al., 2006) 2. (Loudon & Roberts, 1967) 3. (Hsu, et al., 1994) 4. (Choi & Kim, 2007) 5. (Yeager, et al., 1967) 6. (Chao, et al., 2009) Table 2-4 Parameter IF Parameter Sensitivity(Impact factor) cough frequency 6 particle distribution 96 pulmonary rate 1 pathogen concentration 5495  After investigating the uncertainty level and sensitivity of parameters, the order to set optimal parameter values are as follows: (1) Setting as a fixed value for all testing cases:  Exposure time, room size and ventilation rate; (2) Testing all most possible values: cough frequency, particle distribution and pulmonary rate;  33  (3) Calculating the value from the model by setting the output result as close as possible to the best fitting line, ܫ݂݊݁ܿݐ݅݋݊ ܴ݅ݏ݇ = 0.0047, and comparing with published value: pathogen concentration. Here, taking the aircraft as an example and nine hours as the exposure time, eleven cases are used to determine the optimal parameter set. The details are tabulated in the following table. For all the testing case, the exposure time is 9 hours; ventilation rate is at 1052 m3/hour (Wang, et al., 2006) and the space size is 420.5  m3. Detailed calculation for cabin space volume is illustrated in Appendix B.  Table 2-5 Cases summary for optimal parameter value selection Case ID cough frequency (times/hour) Chao weighted distribution with different volume for a single cough pulmonary rate (m3/hour) pathogen concentration (mL-1) 1 3 Duguid1 0.9 2.9956E+07 2 3 LR2 0.9 3.3700E+07 3 3 Chao3 0.9 6.5584E+07 4 3 Zhu4 0.9 5.7619E+07 5 3 Duguid 1.8 1.4978E+07 6 3 LR 1.8 1.6850E+07 7 3 Chao 1.8 3.2792E+07 8 3 Zhu 1.8 2.8810E+07 9 12 Duguid 0.9 7.5533E+06 10 12 LR 0.9 8.4973E+06 11 12 Chao 0.9 1.6537E+07 12 12 Zhu 0.9 1.4528E+07 Notes 1. (Duguid, 1946) 2. (Nicas, et al., 2005) 3.   (Chao, et al., 2009) 4.   (Zhu, et al., 2006)  Considering the pathogen concentration is within the range 6.6x104 - 3.4x107 ml-1 and the mean of 8.4x106 ml-1 (Yeager, et al., 1967), except Case 3 and 4, all other cases are within the range and can be used as optimal parameter sets. All the parameter sets will result the same model  34  output. In the following calculation, Case 10 is selected as the sample input with no particular preference. In reality, there are infinite sets of parameter sets or combination can be used as model input. These selections are based on assumptions introduced in this thesis and literature; thus, they may vary when making different assumptions or with more accurate pathogen concentration. Based on the above investigation, the total dose of pathogen deposited is primarily determined by the product of the total volume of the particles and pathogen concentration. For TB, the calculated dose of pathogen is about 0.475. In particular, when one set of parameters could output the total deposited dose of pathogen is 0.475 at initial state, this set of parameter can be used as optimal parameter set for estimating. 2.2.3 Results and discussion for aircraft cases To compare the modeling results with the actual outbreaks, along with the upper and lower bound of modeling results, a figure is attached as follows:  35   Figure 2-7 Actual outbreak infection risk compared with upper and lower bound of modeling results As shown in the above figure, approximate 72% of actual outbreaks fall between the range of modeling output. The following table summarizes the inputs for upper and lower bound calculations. Table 2-6 Model inputs of upper and lower bound for TB outbreaks Parameter Upper bound Lower bound particle volume Duguid  (Duguid, 1946) Zhu (Zhu, et al., 2006) pulmonary rate (m3/h) 1.8 (Heyder, et al., 1986) 0.9 (Heyder, et al., 1986) pathogen concentration (cfu/ml) 3.4 x 10 7 (Yeager, et al., 1967) 6.6 x 104 (Yeager, et al., 1967) Space volume (m3) 420.5 420.5 Exposure time (hour) 24 24 Infector (#) 1 1 Ventilation rate (m3/hour) 1052 (Wang, et al., 2006) 1052 (Wang, et al., 2006)   36  Nineteen TB outbreaks were collected originally to determine the optimal parameter sets. Only eleven are used here because the scenario of these cases better match the design scope. For instance, in Case 4 and 5, the patients had been transferred from one ward to another. With unknown specific patient room condition, these cases are eliminated. For Case 7, 8 and 9, train and bus were the outbreak location; therefore, these cases are excluded as well. In Figure 2-8, modeling results are compared to actual outbreaks and Wells-Riley equation. According to literature, quanta generation rate for TB can be assumed within range of 1.25 to 60 quanta per hour (q/hr) (Noakes & Sleigh, 2009). Applying the exposure time and ventilation rate of each individual outbreak to Wells-Riley equation, infection risks are calculated based on 1.25 and 60 quanta per hour respectively, which are shown in Figure 2-8.  Figure 2-8 Actual infection risk vs. modeling results and Wells-Riley equation results Based on the observation, in Figure 2-8, the modeling results for all cases are within Wells-Riley estimations (between q=1.25 and 60 q/hr) and even closed the lower bound, q=1.25 q/hr. In order to compare actual outbreaks with Wells-Riley equation, the average quanta generation for TB is 0 10 20 30 40 50 60 70 0 5 10 15 20 In fe ct io n Ri sk  (% ) Exposure Time (hour) Actual outbreaks Modeling results Wells-Riley (q=1.25 q/hr) Wells-Riley (q=60 q/hr)  37  calculated, which is 30.6 q/hr. The model and Wells-Riley are based on well-mixed ventilation in this calculation. Compared to Wells-Riley estimation, modeling results show better prediction for about 63% cases overall (seven out of eleven cases, as highlighted in blue in Table 2-7). Based on the results shown in Table 2-7, with increasing exposure time, the modeling estimation is more accurate in general. Particularly, from 0.5 to 14 hours, the difference between modeling results and actual outbreaks decreased from 100% to 10%. There are exceptional cases, such as: the case with 18 hour exposure. For Wells-Riley equation, with increasing exposure time, the range of calculated infection risk is increasing as well. Therefore, the accuracy of Wells-Riley is case-dependent. Table 2-7 Actual outbreaks vs. modeling results & actual outbreaks vs. Wells-Riley Exposure (hr) Q (m3/hr) ൬ ۻܗ܌܍ܔܑܖ܏ ܀܍ܛܝܔܜܛ − ۯ܋ܜܝ܉ܔ ۽ܝܜ܊ܚ܍܉ܓܛ ۯ܋ܜܝ܉ܔ ۽ܝܜ܊ܚ܍܉ܓܛ ൰ ൬ ܅܍ܔܔܛ − ܀ܑܔ܍ܡ (܉ܞ܍ܚ܉܏܍) − ۯ܋ܜܝ܉ܔ ۽ܝܜ܊ܚ܍܉ܓܛ ۯ܋ܜܝ܉ܔ ۽ܝܜ܊ܚ܍܉ܓܛ ൰ 14 1052 -0.1 3.0 1.25 1052 -0.9 -0.2 8.63 1052 -0.3 2.4 9 1052 0.8 7.8 0.5 1052 -1.0 -0.7 8.5 1052 -0.7 0.3 18 1052 2.9 14.7 8 5460 0.6 7.0 1.75 7560 -0.8 0.3 2 7560 -0.7 1.0 8.75 7560 -0.3 2.3   Uncertainty discussion All the TB outbreaks took place on the airplane with only one infector initially. The uncertainties of the modeling are mainly caused by three factors. The first one is how to determine the actual infection risk. Previous discussion shows that the response percentage among entire passengers  38  to the "after flight survey" is essential to the infection risk values. The value used later for modeling comparison could be varied from the true outbreaks. The Second error introduced into the final modeling results is the method used to determine the best fit line for actual outbreak cases. As shown in the preliminary results, at the first 24 hours, at least, the infection risk starts from origin and increases linearly. While forcing the linear best fit line passes through the point (0,0), larger variance is expected compared with the best lines passes without point (0,0). The last but not least reason of the calculation variance is the optimal parameter selection process. So far, this process is only based on 11 TB outbreaks, by increasing the number of TB outbreaks in the databases, the optimal values might be different. 2.3 Summary of model development and validation In this chapter, a mathematical model is established to predict the infection risk for airborne diseases. Starting from the Wells-Riley model to the spatial infection risk model, detailed information has been given on each parameter involved. In general, the model is designed for evaluating the ventilation system rate and type regarding control of airborne transmitted diseases. To accomplish this task, the model is further developed and completed using sample diseases: TB and influenza. Eleven TB outbreak infection risks are calculated as reference for modeling results comparison. As a result, the best fit line, ܲ = 0.0047ݐ, where P is the infection risk and t is the exposure time, is obtained from the actual outbreak infection risks. By investigating the uncertainty level and sensitivity of parameters, the optimal parameter sets are determined. In particular, parameters are categorized into three groups. Parameters in the first group can be assigned a fixed value for all testing cases. This group includes exposure time, room size, and ventilation rate. The second group is tested for most possible values. Cough frequency, particle distribution, and pulmonary rate belong to this group. Pathogen concentration falls into the third  39  group. Due to extremely high level of uncertainty for pathogen concentration, this parameter is used as decision making factor. As a result, ten groups of parameter input settings are selected as optimal input setup. Taking one set of parameter setting to test the sample inpatient room case, which are Loudon and Roberts distribution, pathogen concentration at 8.4973 x 106 cfu/ml-1, cough at 12 times/hour, pulmonary rate at 0.9 m3/hour and alveolar is the target deposition region. The actual outbreaks are compared with modeling and Wells-Riley estimations. As a result, the modeling results are more accurate than Wells-Riley's, while 30.6 quanta per hour is set as the quanta generation rate for TB. Considering 1.25 to 60 is the quanta generation rate range, modeling results are within the range of Wells-Riley prediction and more closer to the lower bound. Based on the observation, Wells-Riley equation tends to overestimate TB infection risk compared to modeling results.   3 Res To inves examined patient's Figure 3- Figure 3-1 room setting  For each one zone infection room int meters in and lowe each zon exhaust, neglected  ults and tigate the sp  for DV and bed; the oth 1 for patien Schematic for  which the visit room setting  refers to  risk is the o three horiz  height, the r zone (Zon e, the infecti nurse and t  from the sc  discus atial infecti  mixing ven er one is a t, nurse, visi two room setti or is standing aw , infection the entire r same everyw ontal ident  three layers e 1). Refer on risk pred he visitor's hematic. sion on risk in o tilation. In  visitor sta tor, air supp ngs "A" is the ay from the be risk is calcu oom being here within ical layers.  are also na  to Figure 3 icted by the location is rder to locat particular, o nding away ly and exhau room setting wh d. lated for one considered  the room. Since this ro med: upper -2. Assumin  model is co exactly the e high risk ne layout is  from the p st locations ich the nurse i  zone, three as one zon "Three-zon om is a typ  zone (Zone g particles nsistent wit same as the zones, two  a nurse stan atient's bed . s standing besid  zones and n e; therefore e" is define ical inpatie  3), breathin are uniform hin the zone  "One-zone room layout ding close t . Please ref e patient's bed; ine zones. H , the calcu d as dividin nt room tha g zone (Zo ly distribut . The air su " case thus 40 s are o the er to   "B" is ere, lated g the t is 3 ne 2) ed in pply,  it is  41   Figure 3-2 Schematic for 3 zones "Nine-zone" is based on "Three-zone" case but with additional three vertical layers(Figure 3- 3).  Figure 3-3 Schematic for 9 zones As for the "Three-zone" case, by assuming particles are evenly distributed in each zone, the infection risk estimated is the same within each zone but may vary between different zones. The air supply, exhaust, nurse and the visitor's location is exactly the same as the "One-zone" case thus it is also neglected from the schematic. In order to investigate the relationship between cough air jet direction and infection risk, the infection risk for two different cough air jet directions are also calculated and compared.  42  Specifically, one cough air jet direction is horizontal, which happens most likely when the patient sitting on the bed. The other cough air jet direction is vertical. This is assumed that the patient lies on the bed and coughs with mouth open towards the ceiling. Knowing that there is still a significant number of existing inpatient rooms that are vented using mixing ventilation systems, the infection risk is calculated for this room setting at different air exchange rates.  3.1 Infection risk for an inpatient room under DV and mixing system To be able to investigate and compare different room settings and ventilation systems easily, this section presents the modeling results in two general categories based on cough air jet direction: horizontal and vertical. Referring to Table 3-1, TB is used as sample disease here. Short term and long term exposure are defined as 7.3 minutes and 24 hours in this section. Here, the short term exposure time selection is based on CFD simulation results for DV, which records particles information start from initial and up to 440 seconds. Due to the CFD simulation initial setup, the injection takes place within the first couple seconds. As the CFD reports data using 10 seconds as the time interval, the infection risk is estimated starting from 10 seconds after the cough. This point is also set as the initial time for all the presentation of modeling results. There is no particular reason in the choice of setting 24 hours as the long term exposure time. This set up can be varied with different modeling scope or investigation purpose. The total volume of the room is 60 m3. (3x4x5 = 60 m3). The ventilation rate is fixed at 4 ACH, which is the standard operation rate for a typical inpatient room (with displacement ventilation) (Ninomura & Bartley, 2001). The selection for  43  cough frequency, pulmonary rate, pathogen concentration and particle distribution have already been presented in Chapter 2. These inputs will be used for all the case calculations in Section 3.1. Table 3-1 Model input for DV horizontal cough sample disease TB exposure time 7.3 minutes or 24 hours space size (m3) 60 ventilation rate (ACH) 4 cough frequency (times/hour) 3 or 12 pulmonary rate (m3/hour) 0.9 pathogen concentration (ml-1) 8.50 x 106 particle volume Loudon and Roberts  (Nicas, et al., 2005)  3.1.1 Coughing horizontally To compare the infection risk of the two room settings, Figure 3-4 presents modeling results for short time exposure, 7.3 minutes.  44    Figure 3-4 Infection risk for one zone when coughing horizontally (a single cough) "A" series is the result for a nurse standing besides the bed; "B" series is the result for a visitor standing away from the bed; A-1 and B-1 are schematics for the room configuration; A-2 and B-2 are the volume of remaining particles in the room; A-3 and B-3 are the infection risk results due to particles in different size bins and DV and mixing ventilation system  45  As shown in the Figure 3-4, the black triangle and blue square lines in A-2 and B-2 are the volume of the particles remaining in the room for DV and mixing ventilation, respectively. Since the particle removal rate for mixing ventilation is calculated based on Purge Equation (Equation 7), the blue lines are expected to be the same for both setups, which matches the observation. Using the blue square lines as reference, notice that DV is more efficient in terms of particle removal when nurse is standing beside the bed. The possible reason for this finding is that the thermal plume generated by the nurse and the visitor may attract the particles. Assuming particles are ideally and uniformly distributed in the room for mixing ventilation,  and based on the observation from the figure, DV is more efficient in particle removal when nurse stands beside the bed, which compared to the visitor stands away from the bed. Note that the value estimated here for infection risk may vary from the actual values due to the assumptions made for parameters inputs, but the patterns for the overall results would not change. For instance, if pathogen concentration is set at 3.4 x 107 ml-1 instead of 8.5 x 106 ml-1, the magnitude of the infection risk would increase for all predictions; however, the estimated infection risk for DV is still lower than that for the mixing ventilation when a nurse is standing beside the bed. Therefore, it is safe to reach the conclusion that a nurse's or visitor's location in the patient room is essential in terms of controlling infection risk. It is not true, at least for DV, that the further away from the patient's bed and the lower it is the possibility of getting infected . As shown in the A-3 and B-3, Figure 3-4, Size bin 2 contributes the most to the overall infection risk, followed by Size bin 3, 4 and 1. Therefore, reducing the particles in Size bin 2 would be more effective at reducing infection risk compared to reducing other particle sizes. This information can be used as reference for filter selection when designing the inpatient room or similar environment.  Figure 3- For "nur under DV the visito highest r results th the exhau  Figure 3-5 for a nurse configuratio 5 presents th se standing  and mixin r, Figure 3 isk, and Zon at for a typi st compared Infection risk f standing beside n, for bed, patie e prediction beside the g ventilatio -5 B. For b e 1 is the l cal inpatient  to people w or 3 zones with s the bed; B is nt, nurse and vis  of infectio bed" case, n is about 2 oth of the r owest risk z  room, the i ho stand cl  24 hours exp the infection ris itor's locations, n risk for "T in Figure 3- 3% and 40% oom setting one. This o nfection risk ose to the ex osure when cou k estimation for  please refer to F hree-zone" 5 A, the po ; it is appr s, Zone 2, bservation m  is higher w haust for D ghing horizon  a visitor stand igure 3-1 case with 24 ssibility of oximately 3 the breathin atches sho hen people V. tally A is the in ing away from  hours expo  getting inf 8% and 40% g zone, ha rt term exp stand away fection risk esti the bed; C is th 46 sure. ected  for s the osure from  mation e zone  47  To investigate a more specific distribution profile of infection risk, the "Nine-zones" configuration is applied, referring to Figure 3-6 C. For "nurse close to bed" case, Zone 5 is the breathing zone for the patient and also the origin of cough particles released. Zone 2, the breathing zone for the nurse, also has the highest infection risk, as shown in Figure 3-6 A. After 24 hours exposure, the infection risk is about 38%, which is very close to the mixing ventilation prediction, 40%. Infection risk in each zone under DV in this case is lower than that for mixing ventilation. The ranking of the estimated infection risk for DV "Nine-zone" case from highest to lowest is Zone  2, 6, 3, 5, 8, 9, 1, 4 and 7. Noticing Zone 2, 6, 3 and 5 are the zones closest to the nurse and patient; Zone 1, 4 and 7 are the zones closest to the ground and have lower risk. This observation matches with the particle movement trend that particles with <20 µm aerodynamic diameter most likely flow with air stream rather than gravity. Among all zones, predictions of infection risk for Zone 2, 3 and 6 under DV are higher than when treating the entire zone as one zone, the black triangle line in Figure 3-6 A. In Figure 3-6 B, the bottom right figure in Figure 3-6, since the visitor's thermal plume would attract particles, Zone 5 becomes the high risk zone, followed by Zone 2, 8, 6, 9, 4, 7, 3 and 1. Compared to "nurse stands beside the bed" case, after 24 hours exposure, infection risk in Zone 8 increases from about 5% to 27%; vice versa, it reduces from about 26% to 4% for Zone 3. The cause for these variances is the disturbance to the air stream pattern due to heat release from people's bodies as discussed before.     Figure 3-6 for a nurse configuratio As shown risk zone wall and when vis risk of vi visitor's b 6 A. The Infection risk f standing beside n, for bed, patie  in Figure 3 s compared above the p itor stands a sitor's case reathing zo refore, if v or 9 zones with s the bed; B is nt, nurse and vis -6, under D to the zones atient's hea way from t is higher tha ne, Zone 8 i isitor is the  24 hours exp  the infection itor's locations, V, breathing  close to the d, cough par he bed. Und n the nurse n Figure 3-6  only person  osure when cou risk estimation  please refer to F  zones for b  ground. Be ticles canno er this circu 's case, the  B, than nu  present in ghing horizon for a visitor sta igure 3-1 oth the nurs cause the e t be remov mstance, a infection ris rse's breathi  the room b tally A is the in nding beside t e and the vi xhaust is loc ed from the lthough the k are consid ng zone, Zo esides the fection risk esti he bed; C is th sitor are the ated on the  room effici overall infe erably lowe ne 2 in Figu patient, stan 48  mation e zone  high back ently ction r for re 3- ding  49  away from the bed is a solution to lower the possibility to get infected. This conclusion is beneficial for future room setting design, e.g. the visitor's location,  and the decision making process of the exhaust fan's location assuming all other parameters are fixed, e.g. the ventilation rate.  3.1.2 Coughing vertically The same analysis, as in Section 3.1.1, is performed for the case when patient lies on the bed and coughs with mouth opening towards the ceiling, vertically to the ground. Two types of ventilation, DV and mixing ventilation, and room settings, nurse standing beside the bed and visitor standing away from the bed, are considered here. Please review Section 3.1 for parameter inputs selection, zone configurations and modeling assumptions.   Figure 3-7 besides the configuratio particles in Infection risk f bed; "B" series n; A-2 and B-2 different size bin or one zone w  is the result fo  are the volume s and DV and m hen coughing v r a visitor stan  of remaining p ixing ventilatio ertically (a sin ding away from articles in the ro n system gle cough)"A" s  the bed; A-1 om; A-3 and B eries is the resu and B-1 are sch -3 are the infec lt for a nurse st ematics for the tion risk results 50  anding  room  due to  51  Based on the above figures, particles are removed from the room very quickly under DV. After approximately three minutes, the remaining volume of particles is close to zero. Due to the thermal plume generated by the nurse and the visitor, the particle removal rate is slightly slower for the visitor case. The infection risks under DV for both room settings, as expected, are significantly different. After 7.3 minutes of exposure, the infection risk for mixing ventilation is about 0.07%; for DV with the nurse and visitor room settings, it is about 0.004% and 0.008%. Particles in Size bin 2 still contribute the most towards the overall infection risk for DV. The following figure presents the infection risk for "Three-zone" configuration at 24 hours exposure. For mixing ventilation, the possibility of getting infection is about 40%. For DV with the nurse and visitor case, the overall infection risk, considering the entire room as one zone, is about 2% and 4%. Zone 3 is the highest risk zone, followed by Zone 2 and 1. Compare this observation with that from the previous section, the initial cough jet has a profound impact on the infection risk in general.  Figure 3-8 nurse stand configuratio The follo zones, as same as highest r 9%; for a Infection risk f ing besides the n, for bed, patie wing figur  shown in th the previou isk zone is Z ll other zon or 3 zones with bed; B is the nt, nurse and vis e presents t e Figure 3- s "Three-zo one 6 for b es, it is less  24 hours expo infection risk e itor's locations, he infection 9 C. As exp ne" case, w oth nurse an than about 2 sure when coug stimation for a  please refer to F  risk while ected, the in hich is ab d visitor ca % and 4%. hing vertically  visitor standin igure 3-1  dividing t fection risk out 40% af ses with DV   A is the infecti g away from th he room in  for mixing ter 24 hour , which are on risk estimatio e bed; C is th to nine iden ventilation s exposure.  at about 7% 52  n for a e zone tical is the  The  and  Figure 3-9 nurse standi for bed, pati In conclu ventilated mixing v  3.2 Ve In this se of infecti Infection risk f ng besides the b ent, nurse and v sion, when  with the D entilation. T ntilation ction, the di on risk will or 9 zones with ed; B is the infe isitor's locations the patient V, the infe he zone abo  rate vers scussion reg be carried o  24 hours expo ction risk estim , please refer to coughs with ction risk i ve the patie us viabil arding whe ut. sure when coug ation for a visito  Figure 3-1  mouth open s much low nts head is t ity ther the viab hing vertically r standing besid ing toward er compare he highest ri ility can be  A is the infecti e the bed; C is t s the ceiling d with mod sk zone.  neglected i on risk estimatio he zone configu  and the roo eling result n the calcul 53  n for a ration, m is s for ation  54  In order to only investigate ventilation rate's impact on the modeling of infection, a typical 3x4x5m inpatient room is selected as sample space. Assuming the room is ventilated by mixing ventilation system, which is the only force to remove the particles from the system; specifically, the evaporation, condensation and deposition effects are neglected. By treating the entire room as one zone, all the particles are assumed to be uniformly distributed in the space at any time. A summary of parameter inputs is detailed in Table 3-2. This set of parameter inputs is the optimal selection, as discussed in Chapter 2. Table 3-2 Model input for different ventilation rate case sample disease TB exposure time (hours) 24 space size (m3) 60 ventilation rate (ACH) 1,2,..., 8 cough frequency (times/hour) 12 pulmonary rate (m3/hour) 0.9 pathogen concentration (ml-1) 8.50E+06 particle volume  Loudon and Roberts     55   Figure 3-10 Infection risk for different air change rate with mixing ventilation system and 24 hours exposure As shown in Figure 3-10, as the air exchange rate decreases, the infection risk increases with time exposure more quickly. At 1 ACH, after 24 hours exposure, the infection risk is about 87%; and at 8 ACH with the same time exposure, the infection risk is about 23%. At 4 ACH, which is also the standard operation rate for a typical inpatient room, the infection risk is about 40%. To investigate the impact on the modeling results by varying bio-properties, viability is used as the sample property. Here, viability is expressed as follows: ܵ(ݐ) = ܥ௢exp (−ܽݐ)                                                        (14) Where ܵ is the viability, ܽ is the pathogen viable decay rate and ݐ is the exposure time. The a value is selected based on the life time of TB pathogen under this environmental condition. When its life time is 5s, 8 hours, 24 hours or infinity, a is 1.38, 2.4e-4, 8e-5, or 0 respectively.  56   Figure 3-11 Infection risk at different viability under ACH=1, 4 and 8 for the well-mixed room As shown in Figure 3-11, when the viability decay rate is equal to 1.38, which means 99.9% of pathogen lose their viability after 5s, the infection risk is always 0. With increments of the ventilation rate, the viability has less impact on infection risk. The infection risk varies faster in terms of viability at the lowest ventilation rate, i.e. ACH=1. However, when ventilation rate increase to the standard value, i.e. ACH=4, the viability has far less impact on the infection risk. When the ventilation rate becomes even higher, i.e. ACH=8, the viability's impact is negligible. Therefore, viability's impact on infection risk is not significant with standard or higher ventilation rate.  57  Recalling the case discussed in Section 3.1.1 that when patients cough horizontally, infection risk is further calculated applying different decay rates. The model input is listed in Table 3-2. The results shown in Figure 3-12 and Figure 3-13 are based on the assumption that the entire room is one zone.  Figure 3-12 Infection risk for coughing horizontally (nurse stands beside the bed) for DV and well-mixed cases  58   Figure 3-13 Infection risk for coughing horizontally (visitor stands away the bed) for DV and well-mixed cases Again, as shown in the above figures, when the viability decay rate is equal to 1.38, infection risk in both condition is about 0% after 24 hours exposure. In this case, the ventilation rate can be set closely to a normal room due to the pathogen has possibly already lost the infectivity while reaching the susceptible hosts. Based on the observation, excepting the extreme case that pathogen loses viability rapidly, infection risk is highly dependent on the concentration of particles. Therefore, to reduce airborne infection risk, HVAC system should be designed with emphasis on removing particle from breathing zones.  3.3 Summary of infection simulations According to the investigation performed for DV and mixing ventilations, along with the two room settings, which are the nurse standing beside the patient's bed and visitor standing away  59  from the bed, a general conclusion can be reached that the location of people and exhaust fan have impact on the infection risk. The breathing zone for both room settings has higher risk compared to the zones close to the ground. In particular, when cough jet releases horizontally and with DV, the infection risk for the nurse and the visitor cases after 24 hours of exposure is about 23% and 38%, while considering the entire room as one zone. Another profound effect on the overall estimation is the cough releasing direction. For DV, when cough jet is released towards the ceiling, the infection risk is significantly reduced compared with the jet being released horizontally. For instance: with 24 hours exposure and treating the room as one zone, the infection risk is at about 23% for coughing horizontally and about 2% for coughing vertically when nurse is standing beside the bed. By comparing the modeling results and Wells-Riley equation's with actual outbreaks, Wells- Riley tends to overestimate for most of cases while 30.6 quanta per hour is considered. The modeling results are within the range of Wells-Riley equation's estimation for TB transmission and closer to Wells-Riley's lower bound. Based on the observation, for most of cases, with increasing the exposure time, the model output is more accurate. However, due to high variance of environmental conditions, pathogen infectivity, viability and concentration in respiratory fluid, the accuracy of model outputs is varied from case to case. With decreasing the air change rate, the infection risk changes faster while applying  different viabilities. However, excepting the extreme case that  ventilation rate is really low, such as ACH=1, the impact on infection risk due to viability is not significant. Therefore, it is valid that for HVAC designers to design a system based on ventilation rate regarding airborne diseases control.   60  4 Conclusions and future work 4.1 Conclusions A dose-response mathematical model is further developed based on Sze To's model (Sze To & Chao, 2009). This model can be used to investigate spatial infection risk distribution in a closed space with mechanical ventilation system. Using the Wells-Riley equation as foundation, the model further adds bio-properties into the calculation. Whereas Wells-Riley equation uses quanta to express the pathogen generation rate, the model determines the pathogen generation rate based on the concentration of the pathogen in the respiratory fluid, the total volume of fluid one cough could release and the cough frequency. Eleven TB aircraft outbreaks are selected to determine the optimal parameter sets for TB infection risk model. As a result, 10 sets of parameters can be used as TB infection model inputs. Among those, one parameter set is selected to perform the calculation. The details of the selected parameter set consist of cough frequency of 12 times/hour, Loudon and Roberts as particle distribution, pulmonary rate at 0.9 m3/hour, and the pathogen concentration at 8.49 x106 ml-1. This set parameter has equal preference as other parameter sets as they will result the same modeling output. The infection risks are estimated and compared for displacement and well-mixed ventilation under two types of room settings and two coughing directions. Particles with diameter between 2.5 to 8µm contribute the most to the overall infection risk (compared to size bin 1 to 4.5 µm, 8 to16 µm and 16 to 24 µm). For well-mixed ventilation, after 24 hours exposure, the possibility of getting infected by TB in a 3m x 4m x 5m inpatient room is about 40% while applying the optimal parameter set mentioned before. For displacement ventilation, when coughing  61  horizontally, the breathing zone for nurse, who stands below the exhaust and close to the patient's bed, is the highest risk zone. After 24 hours exposure, the infection risk is about 37%. When a visitor stands far away from the bed with the same modeling input, the infection risk for the visitor's breathing zone is about 27%. In this case, the zone close to exhaust is the highest risk zone, which is about 57% after 24 hours exposure. The infection risk in the zone close to patient's bed, the breathing zone for nurse in the previous case, is about 42%. Observation shows that the high risk zone for coughing vertically is the same for both the nurse and the visitor case, which is about 7% and 9% after 24 hours exposure. This value is much lower than estimation for coughing horizontally. Therefore, not only the people's locations, but also the cough air jet direction is important in reducing infection risk. Results also show that it is safer when standing further away from the patient's bed if visitor is the only person in the room besides the patient. Based on the observation and comparison of infection risk regarding different ventilation rate and viabilities, excepting the extreme case that the ventilation rate is really low, the ventilation rate has more profound impact on infection risk compared to viability. Therefore, it is valid that designing a health facilities HVAC system with emphasis on particle removing rate regarding airborne diseases control.  4.2 Model strength and limitation The model developed in this thesis is designed with emphasis to investigate the airborne disease infection risk distribution in an enclosed space. With flexibility to adjust the modeling inputs, e.g. ventilation rate, cough frequency and pathogen concentration in the respiratory fluid, the modeling results can be well used for comparison purpose in terms of infection risk control under various ventilation rates and pathogen generation rates. The principle model development  62  is explained in Section 2.1. Following the process described regarding TB modeling in Section 2.2, this model is suitable to investigate various airborne diseases. The actual time to run the model, considering the nurse stands besides the bed and 9-zone cases (discussed in Section 3.1.1) with accessible CFD data, is approximately <30 minutes. This model is therefore could be used as a tool to give the HVAC designer a quick overview of the infection risk distribution. However, with uncertainties of parameters, e.g. pathogen concentration, and assumptions made toward model establishment, this model is not expected to predict the accurate actual possibility for susceptible people to get infected. Furthermore, the model is limited to investigate the infection risk in an enclosed space with limited objects' movement. There only one infector is considered through the entire exposure time. 4.3 Future work and recommendation Further establishing the actual TB outbreaks cases database will help deliver more reliable parameter sets, therefore, improving the accuracy of the model. If time allows, the particle instantaneous movement simulation for displacement ventilation at different air exchange rates can be carried out. Then the model can be used to examine the spatial infection risk distribution further. As natural or hybrid ventilation are suggested methods in reducing the infection risk, the model can be further upgraded to investigate these scenarios. In the future, when there are related updates for bio-properties available, this information should be implemented into the model to obtain more reasonable results. Although with higher time expense, dividing the space into more zones may provide more accurate results. This is a trade-off solution while the modeling scenario gets more complicated. For instance: multiple inpatients ward with more than one visitor.   63  Bibliography Baker, M., Thornley, C., Mills , C., Roberts, S., Perera, S., Peters, J., et al. (2010). 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Building and Environment , 41, 1691-1702.       71  Appendix A: MATLAB code  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %Infection Risk Modeling Project %June 2012 %Chu Lin %UBC MASc candidate %Description: %1. Read particle instantaneous information from ".txt" file at each time %step %2. According to pre-defined zoning information, generate new ".txt" files %for each zone,  which consists  the total particle numbers in each size %bin at each time step %Supporting files: %1. series of particle instantaneous information files %2. the excel file, which consists the model input %% clearall  %Model input ZoneInform=xlsread('Model input.xls',1);  %Input the test case number Case=1;   %e.g. Case 1 is: a nurse stands beside the bed; coughing %horizontally  %Sign model input to variable Vzone=ZoneInform(Case, 5); %number of zones on vertical Rx=ZoneInform(Case, 2); %Room dimension x Ry=ZoneInform(Case, 3); %Room dimension y Rz=ZoneInform(Case, 4); %Room dimension z  %Define time step (this time step is consistent with CFD filds; the actual %time step should be starts from 0s to 440s.) TimeStep=60:10:500;  %Read all CFD files (one loop-one time step) for TS=1:45  % Sign CFD data to variable     [tPxPzPy Xv YvZv D Temp PdenPmassPp A0]=textread(...     ['displacement-nurse-horizontal-transient-2-5-inj-mesh1-1-',... num2str(TimeStep(TS)),'.000.txt'],... '%f %f %f %f %f %f %f %f %f %f %f %f %f','headerlines',21);  CFDdata=[t PxPzPy Xv YvZv D Temp PdenPmassPp A0];     [NumPNumVariable]=size(CFDdata); % calculate the total number of % particles at this time step  %Set initial number of partilces for the entire space %in each size bin as 0 No(1)=0;  %size bin 1 (1~4.5 micron)  72  No(2)=0;  %size bin 2 (4.5~8 micron) No(3)=0;  %size bin 3 (8~16 micron) No(4)=0;  %size bin 4 (16~24 micron)   %Entire space is one zone forZonePP=1:NumP CFDdata(ZonePP,13)=TimeStep(TS);  %collectpartilces in the desired range ifCFDdata(ZonePP, 8)>1*10^-6 &&CFDdata(ZonePP, 8)<=4.5*10^-6 No(1)=1+No(1); elseifCFDdata(ZonePP, 8)>4.5*10^-6 &&CFDdata(ZonePP, 8)<=8 *10^-6 No(2)=1+No(2); elseifCFDdata(ZonePP, 8)>8 *10^-6 &&CFDdata(ZonePP, 8)<=16 *10^-6 No(3)=1+No(3); elseifCFDdata(ZonePP, 8)>16*10^-6 &&CFDdata(ZonePP, 8)<=24 *10^-6 No(4)=1+No(4); end  end  %Generate the .txt consists with particle information, only 1~24 %micron      data2keep=[CFDdata(1,13) No(1) No(2) No(3) No(4)];      dlmwrite('zone1.txt',data2keep,'delimiter','\t','newline','pc','- append');   %Three-zone %Set initial number of partilces for each zone in each size bin as 0 %zone 1 No1(1)=0; No1(2)=0; No1(3)=0; No1(4)=0;  %zone 2 No2(1)=0; No2(2)=0; No2(3)=0; No2(4)=0;  %zone 3 No3(1)=0; No3(2)=0; No3(3)=0; No3(4)=0;   %collectpartilces in the desired range for each zone forZonePP=1:NumP CFDdata(ZonePP,13)=TimeStep(TS); %size bin1  73  ifCFDdata(ZonePP, 8)>1*10^-6 &&CFDdata(ZonePP, 8)<=4.5*10^- 6&&Pz(ZonePP)<=(Rz/Vzone) No1(1)=1+No1(1); elseifCFDdata(ZonePP, 8)>1*10^-6 &&CFDdata(ZonePP, 8)<=4.5*10^- 6&&Pz(ZonePP)<=(2*Rz/Vzone)&&Pz(ZonePP)>(Rz/Vzone) No2(1)=1+No2(1); elseifCFDdata(ZonePP, 8)>1*10^-6 &&CFDdata(ZonePP, 8)<=4.5*10^- 6&&Pz(ZonePP)>(2*Rz/Vzone) No3(1)=1+No3(1);  %size bin2 elseifCFDdata(ZonePP, 8)>4.5*10^-6 &&CFDdata(ZonePP, 8)<=8 *10^- 6&&Pz(ZonePP)<=(Rz/Vzone) No1(2)=1+No1(2); elseifCFDdata(ZonePP, 8)>4.5*10^-6 &&CFDdata(ZonePP, 8)<=8 *10^- 6&&Pz(ZonePP)<=(2*Rz/Vzone)&&Pz(ZonePP)>(Rz/Vzone) No2(2)=1+No2(2); elseifCFDdata(ZonePP, 8)>4.5*10^-6 &&CFDdata(ZonePP, 8)<=8 *10^- 6&&Pz(ZonePP)>(2*Rz/Vzone) No3(2)=1+No3(2);  %size bin 3 elseifCFDdata(ZonePP, 8)>8 *10^-6 &&CFDdata(ZonePP, 8)<=16 *10^- 6&&Pz(ZonePP)<=(Rz/Vzone) No1(3)=1+No1(3); elseifCFDdata(ZonePP, 8)>8 *10^-6 &&CFDdata(ZonePP, 8)<=16 *10^- 6&&Pz(ZonePP)<=(2*Rz/Vzone)&&Pz(ZonePP)>(Rz/Vzone) No2(3)=1+No2(3); elseifCFDdata(ZonePP, 8)>8 *10^-6 &&CFDdata(ZonePP, 8)<=16 *10^- 6&&Pz(ZonePP)>(2*Rz/Vzone) No3(3)=1+No3(3);  %size bin 4 elseifCFDdata(ZonePP, 8)>16*10^-6 &&CFDdata(ZonePP, 8)<=24 *10^- 6&&Pz(ZonePP)<=(Rz/Vzone) No1(4)=1+No1(4); elseifCFDdata(ZonePP, 8)>16*10^-6 &&CFDdata(ZonePP, 8)<=24 *10^- 6&&Pz(ZonePP)<=(2*Rz/Vzone)&&Pz(ZonePP)>(Rz/Vzone) No2(4)=1+No2(4); elseifCFDdata(ZonePP, 8)>16*10^-6 &&CFDdata(ZonePP, 8)<=24 *10^- 6&&Pz(ZonePP)>(2*Rz/Vzone) No3(4)=1+No3(4); end  end       data2keep=[CFDdata(1,13) No1(1) No1(2) No1(3) No1(4)];      dlmwrite('zone_1.txt',data2keep,'delimiter','\t','newline','pc','- append');       data2keep=[CFDdata(1,13) No2(1) No2(2) No2(3) No2(4)];      dlmwrite('zone_2.txt',data2keep,'delimiter','\t','newline','pc','- append');       data2keep=[CFDdata(1,13) No3(1) No3(2) No3(3) No3(4)];  74       dlmwrite('zone_3.txt',data2keep,'delimiter','\t','newline','pc','- append');   end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Infection Risk Modeling Project %June 2012 %Chu Lin %UBC MASc candidate %Description: %1. Calculate the infection risk for entire space (DV), three zones (DV). %and well-mixed ventilation(entire zone).  %Supporting files: %1. the text files contains particle instantaneous location and number of %particle in each size bin %2. the excel file, which consists the model input  clearall  CaseData=xlsread('Model input.xls',7); tb_caseinput=1;               %the total number of cases will be calculated TB_Case=tb_caseinput; %define variables Q=CaseData(TB_Case,6);               %ventilation rate (m^3/s) V=CaseData(TB_Case,4);               %room volume (m^3) S=CaseData(TB_Case,7);               %total number of susceptible (#) I=1;               %total number of infectors (#)  R=1;               % infectivity  f_cough=CaseData(TB_Case,10);              %cough frequency (s/time) pul=CaseData(TB_Case,11);             %pulmonary rate (m^3/h) c_i_pathogen=CaseData(TB_Case,12)*10^6; %(cfu/m^3); T=CaseData(TB_Case,3);               %total duration (s or h)  %Zoning information ZoneInform=xlsread('Model input.xls',1);  Vzone=ZoneInform(1, 5);  %Define line type style={'-','--','-.',':'}; %Define line color color=winter(4);  %Read particle information in the entire zone  75  [TimeStep No_1 No_2 No_3 No_4]=textread('zone1.txt','%f %f %f %f %f');  %Calculate the infection risk for each zone forIIRRzone=1:Vzone  [TimeStep1 No1_1 No1_2 No1_3 No1_4]=textread(['zone_',num2str(IIRRzone),'.txt'],'%f %f %f %f %f');  %total volume at each time step (from 0s up to 440s, CFD data only provide %particle movement information during this time constrain for TT=2:length(TimeStep1) %Based on Loudon and Roberts volume and Chao's distribution         No_(1)=168*0.4*No1_1(TT)/No_1(2)*0.15*1/6*3.14*(((1+4.5)/2)*10^-6)^3;         No_(2)=2311*0.4*No1_2(TT)/No_2(2)*0.3*1/6*3.14*(((4.5+8)/2)*10^-6)^3;         No_(3)=857*0.4*No1_3(TT)/No_3(2)*0.05*1/6*3.14*(((8+16)/2)*10^-6)^3;         No_(4)=287*0.4*No1_4(TT)/No_4(2)*0.01*1/6*3.14*(((16+24)/2)*10^-6)^3; No_total(TT)=sum(No_); end  No_total_end=No_total(TT); %After 440, assuming the remaining particles will be removed from the %system based on purge equation %This "for" loop calculates the total volume of the particles remaining %during this time period. for TT=(length(TimeStep1)+1):(T*360) % 10 second is the time interval     No_total(TT)=No_total_end*exp(-Q/(V/Vzone)*10*(TT-length(TimeStep1))); end  %dose at each time step fortt=2:T*360 %time interval is 10s D(tt)=pul/360*No_total(tt)/(V/Vzone)*c_i_pathogen; end  %accumulative dose for one cough Do=zeros(1,T*360);  fortt=2:T*360 Do(tt)=sum(D(1:tt)); end  %total coughed times during the time exposure f_N=floor(T*360/(f_cough/10));  %matrix for dose of each cough D(time step, ith cough) D_main=zeros(f_N, tt);  %fill the matrix forcoughtimes=1:f_N ifcoughtimes==1 D_main(coughtimes, :)=Do(:); else        D_main(coughtimes,((coughtimes-1)*f_cough/10+1):T*360)=Do(1:(tt- (coughtimes-1)*f_cough/10)); end  76  end  %total dose at time t Dt=zeros(1,tt); fortt=2:T*360 Dt(tt)=sum(D_main(:,tt)); end  %calculate the infection risk at time t P=zeros(T*360,1); fortt=2:T*360 P(tt)=1-exp(-Dt(tt)); end  %plot the result plot((1:10:T*3600)/3600, P*100,'linestyle',style{IIRRzone},'color',color(IIRRzone,:),'LineWidth',2) holdon;  end  %Entire zone (DV) forIIRRzone=1  [TimeStep1 No1_1 No1_2 No1_3 No1_4]=textread('zone1.txt','%f %f %f %f %f'); %total volume at each time step for TT=2:length(TimeStep1) %LR         No_(1)=168*0.4*No1_1(TT)/No_1(2)*0.15*1/6*3.14*(((1+4.5)/2)*10^-6)^3;         No_(2)=2311*0.4*No1_2(TT)/No_2(2)*0.3*1/6*3.14*(((4.5+8)/2)*10^-6)^3;         No_(3)=857*0.4*No1_3(TT)/No_3(2)*0.05*1/6*3.14*(((8+16)/2)*10^-6)^3;         No_(4)=287*0.4*No1_4(TT)/No_4(2)*0.01*1/6*3.14*(((16+24)/2)*10^-6)^3; No_total(TT)=sum(No_); end  No_total_end=No_total(TT);  for TT=(length(TimeStep1)+1):(T*360) No_total(TT)=No_total_end*exp(-Q/V*10*(TT-length(TimeStep1))); % 10 second is the time interval end  %dose at each time step fortt=1:T*360 %time interval is 10s D(tt)=pul/360*No_total(tt)/V*c_i_pathogen; end  %accumulative dose for one cough Do=zeros(1,T*360);  fortt=1:T*360 Do(tt)=sum(D(1:tt)); end   77  %total coughed times during the time exposure f_N=floor(T*360/(f_cough/10));  %matrix for dose of each cough D(time step, ith cough) D_main=zeros(f_N, tt);  %fill the matrix forcoughtimes=1:f_N ifcoughtimes==1 D_main(coughtimes, :)=Do(:); else        D_main(coughtimes,((coughtimes-1)*f_cough/10+1):T*360)=Do(1:(tt- (coughtimes-1)*f_cough/10)); end end  %total dose at time t Dt=zeros(1,tt); fortt=1:T*360 Dt(tt)=sum(D_main(:,tt)); end  %calculate the infection risk at time t P=zeros(T*360,1); fortt=1:T*360 P(tt)=1-exp(-Dt(tt)); end  P(end+1)=P(end); plot((1:3600:T*3600+1)/3600, P(1:360:end)*100,'k-<','LineWidth',2) holdon;  end   %Assuming well-mixed; based on purge equation; well-mixed ventilation %Loudon and Roberts: total volume of the cough fluid; Chao's distribution No(1)=168*0.4*0.15*1/6*3.14*(((1+4.5)/2)*10^-6)^3; No(2)=2311*0.4*0.3*1/6*3.14*(((4.5+8)/2)*10^-6)^3; No(3)=857*0.4*0.05*1/6*3.14*(((8+16)/2)*10^-6)^3; No(4)=287*0.4*0.01*1/6*3.14*(((16+24)/2)*10^-6)^3;  forTB_Case=tb_caseinput  No_total(TB_Case)=sum(No)/V;  totaltimestep=T*3600;  %particle numbers (density) fortt=1:T*3600 D(tt)=pul/3600*No_total(TB_Case)*c_i_pathogen*exp(-Q/V*tt); end  %accumulative dose for one cough  78  Do=zeros(1,T*3600);  fortt=1:T*3600 Do(tt)=sum(D(1:tt)); end  %total coughed times during the time exposure f_N=floor(T*3600/f_cough);  %matrix for dose of each cough D(timestep, ith cough) D_main=zeros(f_N, tt);  %fill the matrix forcoughtimes=1:f_N ifcoughtimes==1 D_main(coughtimes, :)=Do(:); else        D_main(coughtimes,((coughtimes-1)*f_cough+1):T*3600)=Do(1:(tt- (coughtimes-1)*f_cough)); end end  %total dose at time t Dt=zeros(1,tt); fortt=1:T*3600 Dt(tt)=sum(D_main(:,tt)); end  %calculate the infection risk at time t P=zeros(T*3600,1); fortt=1:T*3600 P(tt)=1-exp(-Dt(tt)); end  plot((1:3600:(T*3600+1))/3600, P(1:3599:end)*100,'b-s','LineWidth',2) holdon; end  xlabel('Exposure Time (hour)','FontSize',14); ylabel('Infection Risk (%)','FontSize',14); set(gca,'Fontsize',12)  Size_legend=legend('zone 1 @ DV', 'zone 2 @ DV', 'zone 3 @ DV','entire space/one zone @ DV', 'entire space/one zone @ mixing','location','northwest'); set(Size_legend,'FontSize',12)  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Infection Risk Modeling Project %June 2012 %Chu Lin  79  %UBC MASc candidate %Description: %1. Calculate the particle volume remove rate for each size bin under DV %Supporting files: %1. the text file contains particle numbers in each size at different time %step %2. the excel file contains the model input  clearall  %Read data [TimeStep No_1 No_2 No_3 No_4 ]=textread('zone1.txt','%f %f %f %f %f');  %Initiate variables SizeBin1=zeros(1,length(TimeStep)); SizeBin2=zeros(1,length(TimeStep)); SizeBin3=zeros(1,length(TimeStep)); SizeBin4=zeros(1,length(TimeStep)); Tzone=zeros(1,length(TimeStep));  %Chao's distribution & Loudon Roberts's volume No(1)=168*0.4*0.15*1/6*3.14*(((1+4.5)/2)*10^-6)^3; No(2)=2311*0.4*0.3*1/6*3.14*(((4.5+8)/2)*10^-6)^3; No(3)=857*0.4*0.05*1/6*3.14*(((8+16)/2)*10^-6)^3; No(4)=287*0.4*0.01*1/6*3.14*(((16+24)/2)*10^-6)^3; No_total=sum(No);  %Calculate volume remaining in the space for each zone for ii=2:length(TimeStep) SizeBin1(ii)=No_1(ii)/No_1(2)*168*0.4*0.15*1/6*3.14*(((1+4.5)/2)*10^-6)^3; SizeBin2(ii)=No_2(ii)/No_2(2)*2311*0.4*0.3*1/6*3.14*(((4.5+8)/2)*10^-6)^3; SizeBin3(ii)=No_3(ii)/No_3(2)*857*0.4*0.05*1/6*3.14*(((8+16)/2)*10^-6)^3; SizeBin4(ii)=No_4(ii)/No_4(2)*287*0.4*0.01*1/6*3.14*(((16+24)/2)*10^-6)^3; Tzone(ii)=(SizeBin1(ii)+SizeBin2(ii)+SizeBin3(ii)+SizeBin4(ii)); end  %Define line color and type color=winter(4); style={'-','--','-.',':'};  %plot plot(TimeStep(2:end)/60- 1,SizeBin1(2:end),'linestyle',style{1},'color',color(1,:),'LineWidth',2) holdon; plot(TimeStep(2:end)/60- 1,SizeBin2(2:end),'linestyle',style{2},'color',color(2,:),'LineWidth',2) holdon; plot(TimeStep(2:end)/60- 1,SizeBin3(2:end),'linestyle',style{3},'color',color(3,:),'LineWidth',2) holdon; plot( TimeStep(2:end)/60- 1,SizeBin4(2:end),'linestyle',style{4},'color',color(4,:),'LineWidth',2) holdon; plot(TimeStep(2:end)/60-1,Tzone(2:end),'kv','LineWidth',2); holdon  80    %Well-mixed; CaseData=xlsread('April.xls',2); TB_Case=1; Q=CaseData(TB_Case,6);               %ventilation rate (m^3/s) V=CaseData(TB_Case,4); Prate=zeros(1,length(TimeStep-1));  forjj=1:length(TimeStep-1) Prate(jj)=No_total*exp(-Q(TB_Case)/V(TB_Case)*10*jj); end  plot(TimeStep/60-1, Prate,'bs','LineWidth',2); xlabel('Exposure Time (mins)','FontSize',14); ylabel('Volume of remaining particles in the room (m^3)','FontSize',14); set(gca,'Fontsize',12)  Size_legend=legend('Size bin 1 @ DV', 'Size bin 2 @ DV', 'Size bin 3 @ DV', 'Size bin 4 @ DV','All bins @ DV','All bins @ Purge Equation','location','northeast'); set(Size_legend,'FontSize',12)  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%              81  Appendix B: Airplane cabin space calculation In this paper, Boeing 767 is selected as the sample aircraft type to perform calculation. Boeing 767 is manufactured by Boeing Company and it is aimed for the middle airplane market (200- 250 seats).  Lighter and more efficient than competing jetliners are two key features for Boeing 767s. In order to estimate the cabin space of the Boeing 767, the top view and cross-section view of Boeing 767 are obtained from the company website.  Figure B-1 Top View of Boeing 767 seating options  Figure B-2 Cross-section view of Boeing 767 seating options  82  The interior cabin width is 4.7 m and the total length is 48.5m for Boeing 767-200ER, 54.9 m for Boeing 767-300ER and 61.3 m for Boeing 767-400ER . Assuming the cross of the airplane is a perfect half circle. Thus, the volume of the interior space is calculated as follow: ܸ = ଵଶ గ ସ ܦଶܮ                                                               (B-1) Where ܸ is the interior cabin volume, (m3);ܦ is the cabin width, (m);ܮis the total length, (m). Thus,ܸ is 420.5 m3 for Boeing 767-200ER, 476.0 m3 for Boeing 767-300ER and 531.5 m3 for Boeing 767-400ER.              83  Appendix C: TB outbreak cases TB Case 1 Author M. Miller et. all 1996 Title  Tuberculosis risk after exposure on airplanes Case Year  1993 Location Boeing 747  Specification  Original Data Duration  8 hour 22 mins Room Volume  Boeing 767 Filtration  1. 50% recirculation;  >0.3 um  2. 14~ 22 ACH Total Population 101 Number of Infector 1 Number of Infected  29 Comment 1. The ground time is <45 mins   TB Case 2 Author M. Miller et. all 1996 Title Tuberculosis risk after exposure on airplanes Case Year  1993 Location British Aero space 146  Specification Original Data Duration  1 h 24 mins Room Volume  British Aero space 146 Filtration  1. 40% recirculate;  2. 18 ACH Total Population 20 Number of Infector 1 Number of Infected  6 Comment 1.  At this time, this case is not selected to calculate the infection risk due to the short exposure time (<2hours).      84  TB Case 3 Author Pair Dong Wang Title Two-step tuberculin testing of passengers and crew on a commercial airplane Case Year  2003 Location Commercial flight (from Los Angeles to Taipei, Taiwan)  Specification Original Data Duration  14 Room Volume  Commercial flight Filtration Total Population 225 Number of Infector 1 Number of Infected  173 Comment 1.  Total population did skin test: 225 (1st skin test); 39 (2nd skin test); 24 (3rd skin test); 173 (positive skin test); 11 (2nd skin test); 16 (3rd skin test) (number used in the model) 2. The difference between the skin test is the duration after exposure ( 1st: 3.5 ~ 4.2 weeks; 2nd: 4.7 ~ 6.0 weeks; 3rd: 15.8 ~ 18.8 weeks)    TB Case 4 Author, publish year N. J. Ehrenkranz  1972 Title Tuberculosis outbreak in a general hospital: evidence for airborne spread of infection Case Year  1969 Location general hospital( patient ward)  Specification Original Data Duration  57 hours Room Volume  Patient room on NW 3 Filtration  ward (70% recycling; 30% mix of fresh air) Total Population 60 Number of Infector 1 Number of Infected  21 Comment 1. Case 4 and 5 are the same patient but transferred between rooms 2. Author applied Wells-Riley equation and obtained 60 quanta/h for TB    85  TB Case 5 Author, publish year N. J. Ehrenkranz  1972 Title Tuberculosis outbreak in a general hospital: evidence for airborne spread of infection Case Year  1969 Location general hospital( patient ward)  Specification Original Data Duration  67 hours Room Volume  Patient room Filtration  better ventilated ward (recycle 100% air; frequently opened door 5~6 times /hour) Total Population 19 Number of Infector 1 Number of Infected  19 Comment 1. Case 4 and 5 are the same patient but transferred between rooms  TB Case 6 Author, publish year M. Moore, et al. 1996 Title A passenger with pulmonary/laryngeal tuberculosis: no evidence of transmission on two short flights Case Year  1996 Location airplane  Specification Original Data Duration  1.25 hours Room Volume   airplane Filtration Total Population 120* Number of Infector 1 Number of Infected  5** *110 passenger and 10 crew member ** 5 got positive TST Comment    86  Note: TB Case 7, 8 and 9 were the same person travelled at one time. In the report, the total population, number of infector and number of infected indicated the total number for the entire trip, specifically from Chicago to Pittsburgh, then to Washington and final destination was Florida. TB Case 7 Author, publish year M. Moore, et al. 1998 Title A train passenger with pulmonary tuberculosis: evidence of limited transmission during travel Case Year  1996 Location U.S passenger train ( from Chicago to Pittsburgh)  Specification Original Data Duration  12.3 hours Room Volume   Train Filtration  Without HEPA; ~10 to 15 ACH Total Population 228* Number of Infector 1 Number of Infected  4** *228 (62% passengers, total 479, only 228 located)+29 crew member (66% of total 44); this number combined Case 7,8 and 9 ** 4 ( out of total 16 with positive TST are most likely get infected by the infector); ); this number combined Case 7,8 and 9  TB Case 8 Author, publish year M. Moore, et al. 1998 Title A train passenger with pulmonary tuberculosis: evidence of limited transmission during travel Case Year  1996 Location Bus (from Pittsburgh to Washington)  Specification Original Data Duration  5.5 hours Room Volume   Bus Filtration Without HEPA; ~ 10 to 15 ACH Total Population 228* Number of Infector 1 Number of Infected  4** *  228 (62% passengers, total 479, only 228 located)+29 crew member (66% of total 44); this number combined Case 7,8 and 9 ** 4 ( out of total 16 with positive TST are most likely get infected by the infector); ); this number combined Case 7,8 and 9   87   TB Case 9 Author, publish year M. Moore, et al. 1998 Title A train passenger with pulmonary tuberculosis: evidence of limited transmission during travel Case Year  1996 Location Train (From Washington to Florida)  Specification Original Data Duration  16.8 hours Room Volume  Train Filtration Without HEPA; ~ 10 to 15 ACH Total Population 228* Number of Infector 1 Number of Infected  4** * 228 (62% passengers, total 479, only 228 located)+29 crew member (66% of total 44); this number combined Case 7,8 and 9 ** 4 ( out of total 16 with positive TST are most likely get infected by the infector); ); this number combined Case 7,8 and 9  TB Case 10 Author, publish year Morbidity and mortality weekly report March 3, 1995 Title Exposure of passengers and flight crew to Mycobacterium tuberculosis on commercial aircraft, 1992-1995 Case Year  1994 Location Airplane (From Chicago to Honolulu)  Specification  Original Data Duration  8.4h Room Volume  Aircraft 174.3 m^3* Filtration 18 ACH* Total Population 257 Number of Infector 1 Number of Infected  15 * Estimated based on a Boeing 767    TB Cas Author, pu Title Case Year Location  Specifica Duration Room Vo Filtration Total Pop Number o Number o *23/212 ( 13/43( fro    e 11 blish year  tion lume  ulation f Infector f Infected TST positive m Aug to Oc  C.R. Driver Transmissio 1992 Large US ai  Original Da May through Aircraft 5 ~ 29 ACH ( 212 crew + 1 (crew mem 23* ; 10/169 from t)  1994 n of Mycoba rline carrier ta  Oct 1992 cabin); 11 ~ 4 59 passenger ber)  May to July cterium tuber 2 ACH (cock s (212 did TS ; 13/43 from culosis assoc pit) T)  Aug to Oct iated with air ) ; The graph   travel  above is sho 88 wing  89  TB Case 12 Author, publish year Morbidity and mortality weekly report March 3, 1995 Title Exposure of passengers and flight crew to Mycobacterium tuberculosis on commercial aircraft, 1992-1995 Case Year  1993 Location Airplane (from London to Minneapolis)  Specification Original Data Duration  9 hours Room Volume  Aircraft Filtration  unknow Total Population 79** Number of Infector 1 Number of Infected  8 * Estimated based on Boeing 767 * Total is 343 people (used as total population in the model), only 79 people did the test Comment 1. All these 8 people have exposed to M. tuberculosis, thus, there is no evidence of transmission of TB during the flight.   TB Case 13 Author, publish year Morbidity and mortality weekly report March 3, 1995 Title Exposure of passengers and flight crew to Mycobacterium tuberculosis on commercial aircraft, 1992-1995 Case Year  1993 Location Airplane (from Mexico to San Francisco)  Specification Original Data Duration  0.5 hours Room Volume  Aircraft Filtration Total Population 22* Number of Infector 1 Number of Infected  10** * 22 out of total 92 people did TST **9 of 10 TST positive people have been infected by TB before flying. Comment 1. Thus, Public health concludes that there is no evidence for TB transmission during the flight.    90  TB Case 14 Author, publish year Morbidity and mortality weekly report March 3, 1995 Title Exposure of passengers and flight crew to Mycobacterium tuberculosis on commercial aircraft, 1992-1995 Case Year  1993 Location Airplane (from Frankfurt Germany to New Your city)  Specification Original Data Duration  8.5 hours Room Volume  Aircraft Filtration Total Population 219 Number of Infector 1 Number of Infected  32 *The values are based on a Boeing 767 aircraft Comments 1. The TST positive and conversions might be associated with prior TB infection. 2. This airline was one-stop flight. The second flight was 1.5 hour from New York City to Cleveland, Ohio. The total population and infected number were the total number for both flights  TB Case 15 Author, publish year Morbidity and mortality weekly report March 3, 1995 Title Exposure of passengers and flight crew to Mycobacterium tuberculosis on commercial aircraft, 1992-1995 Case Year  1994 Location Airplane (from Taiwan -Tokyo - Seattle - Minneapolis -Wisconsin )  Specification Original Data Duration  3 hours +9 hours+3  hours + 3 hours  Room Volume  Aircraft Filtration Total Population 85** Number of Infector 1 Number of Infected  14 *The values are based on a Boeing 767 aircraft ** 85 did TST out of total 661 passengers in 4 flights Comments 1. All 14 people seated more than 5 rows away from the infector. Although there is a possibility of TB transmission during the flight, the positive TST might be resulted from prior M. TB infection.    91  TB Case 16 Author, publish year T. A. Kenyon, 1996 Title Transmission of multidrug-resistant mycobacterium tuberculosis during a long airplane flight Case Year  1994 Location Airplane (from Honolulu to Chicago )  Specification Original Data Duration  8 hours Room Volume  Aircraft Filtration  HEPA; 6~20 ACH; %50 air recirculated Total Population 298 Number of Infector 1 Number of Infected  7 * The values are based on a Boeing 747-100 aircraft    TB Case 17 Author, publish year T. A. Kenyon, 1996 Title Transmission of multidrug-resistant mycobacterium tuberculosis during a long airplane flight Case Year  1994 Location Airplane (from Chicago to Baltimore )  Specification  Original Data Duration  1.75 hours Room Volume  Airbus 320-200 Filtration  HEPA; 6~20 ACH; %50 air recirculated Total Population 104 Number of Infector 1 Number of Infected  4    92  TB Case 18 Author, publish year T. A. Kenyon, 1996 Title Transmission of multidrug-resistant mycobacterium tuberculosis during a long airplane flight Case Year  1994 Location Airplane (from  Baltimore to Chicago )  Specification Original Data Duration  2 hours Room Volume  Airbus 320-200 Filtration  HEPA; 6~20 ACH; %50 air recirculated Total Population 109 Number of Infector 1 Number of Infected  3    TB Case 19 Author, publish year T. A. Kenyon, 1996 Title Transmission of multidrug-resistant mycobacterium tuberculosis during a long airplane flight Case Year  1994 Location Airplane (from  Chicago to Honolulu )  Specification Original Data Duration  8.75 hours Room Volume  Boeing 747-100 Filtration  HEPA; 6~20 ACH; %50 air recirculated Total Population 249 Number of Infector 1 Number of Infected  15* *6 TST positive  of 68 total tested are within the same cabin with patient; 4/13 within 2 rows; 2/55 elsewhere in the same cabin       93  Appendix D: Parameter sensitivity investigation To determine one parameter's Impact Factor (IF), a fixed value is first assigned to the rest parameters; and then the infection risk is calculated and compared based on the possible values for the targeted parameter by using  Equation (13). Table D-1 Cases Summary of Sensitivity Investigation Case ID parameter investigating exposure time room size ventilation rate cough frequency particle distribution pulmonary rate pathogen concentration Calculated infection Risk Impact Factor   hour m3 m3/hour times/hour  m3/hour pfu/ml 1 cough frequency 9 174.6 1052 3 Duguid 0.9 8.4x10^6 0.02711 6.2 2 9 174.6 1052 12 Duguid 0.9 8.4x10^6 0.1954 3 particle distribution 9 174.6 1052 3 Duguid 0.9 8.4x10^6 0.02709 95.9 4 9 174.6 1052 3 Loudon and Roberts 0.9 8.4x10^6 0.007577 5 9 174.6 1052 3 Chao 0.9 8.4x10^6 0.00028 6 pulmonary 9 174.6 1052 3 Duguid 0.9 8.4x10^6 0.02709 1.0 7 9 174.6 1052 3 Duguid 1.8 8.4x10^6 0.05349 8 pathogen 9 174.6 1052 3 Duguid 0.9 10^5 0.01346 5495 9 9 174.6 1052 3 Duguid 0.9 10^6 0.1345 10 9 174.6 1052 3 Duguid 0.9 10^7 1.337 11 9 174.6 1052 3 Duguid 0.9 10^8 12.59 12 9 174.6 1052 3 Duguid 0.9 10^9 73.97   94  Appendix E: Influenza outbreak cases Case 1 Author M. R. Mose et. all 1979 Title An outbreak of influenza aboard a commercial airliner Case Year Location Boeing 737 Specification  Original Data Duration  >3 hours Room Volume  Boeing 737 Filtration  0.0111m3/s * Total Population 53** Number of Infector 1 Number of Infected  38 * for the first 2 hours, the ventilation is off with the door closed ; the ventilation is on after 3 hours, at 0.0111m3/s. ** for <1hour, total population is 15 and 8 people got infected;      for 1~3 hour, total population is 9 and 5 people got infected; for>3 hours, total population is 29 and 25 people got infected.   Thus, among 53 people, 38 got infected.   Case 2 Author A. Ruth Foxwell et. all 2009 Title Transmission of Influenza on International Flight Case Year Location Airbus A380 Specification  Original Data Duration  14 hours Room Volume Filtration Total Population 445* Number of Infector 4** Number of Infected  24*** * among 445 people, only 188 (42%) passengers responded the survey after the flight ** 8 passengers had ILI; 4 of these confirmed had H1N1, 1 is negative, 3 not tested ***24 (ILI <=7 dyas after arriving; 2 confirmed pandemic; 15 negative for H1N1, 7 not tested) Comment 1. 20 (83 % of 24 passengers developing ILI sat in aisle seats, these seat increased the risk of contracting an ILI by 1.8x, survey showed 1.3x)  2. 2x2x2rows zone is considered,  ILI increased 7.7%    95  Case 3 Author A. Ruth Foxwell et. all 2010 Title Transmission of Influenza on International Flights Case Year Location Boeing 747 - 400 Specification  Original Data Duration  7 hours 40 minutes 7.67 hours Room Volume   173.4 m^3 Filtration Total Population 293* 293 Number of Infector 1 1 Number of Infected  6 6 * among 293 people, 131 (45%) people replied the survey Comment 1. the duration is estimated from web information  Case 4 Author A.G. Marsden 2003 Title Influenza outbreak related to air travel Case Year Location Bae 146 Specification  Original Data Duration  3 hours 20 minutes 3.33 hours Room Volume   173.4 m^3 Filtration Total Population 75 75 Number of Infector 1 1 Number of Infected  21 21  Case 5 Author Title Outbreak of 2009 Pandemic influenza A(H1N1)on a Peruvian Navy Ship June-July 2009,2010 Case Year Location Specification  Original Data Duration Room Volume Filtration Total Population 355 Number of Infector 1 Number of Infected  78   96  Case 6 Author K. C. Klontz Title An outbreak of influenza A/Taiwan/1/86 (H1N1) infections at anavlbase and its association with airplane travel Case Year  1986 Location DC-9 airplanes Specification  Original Data Duration  2 hours 30 mins Room Volume Filtration Total Population 34 Number of Infector 8 Number of Infected  18  Case 7 Author K. C. Klontz Title An outbreak of influenza A/Taiwan/1/86 (H1N1) infections at anavlbase and its association with airplane travel Case Year  1986 Location DC-9 airplanes Specification  Original Data Duration  2 hours 30 mins Room Volume Filtration Total Population 43 Number of Infector 3 Number of Infected  5         97  Appendix F: Influenza infection risk modeling and viability study Following the methodology explained in Section 2.2.2, in this Appendix, an infection risk model is developed for Influenza. In Table 1, three influenza outbreaks cases are listed and the actual infection risk is calculated using Equation (10). The Case ID corresponds to case number listed in Appendix E. Table F-1 Actual Influenza outbreaks summary Case ID Exposure time (h) Room Volume (m^3) ACH ventilation rate, Q (m^3/s) Total population Infector people get infected Actual infection risk (%) 1 3 79.5 0.3 0.006625 53 1 38 72% 3 7.67 173.4 18 0.867 131 1 6 5% 4 3.33 99.76 18 0.4988 75 1 20 27%   Figure F-1 Actual Influenza outbreaks infection risk and the trend line As mentioned in Section 2.2.2, the relationship between infection risk and exposure time is linear in the first at least 24 hours. In Figure F-1, the fit to data is poor due to limited data points are applied here. To improve the reliability of this fitting, more actual outbreaks are desired to be used as references. y = 0.043x 0% 10% 20% 30% 40% 50% 60% 70% 80% 0 2 4 6 8 10 In fe ct io n Ri sk  Exposure Time (hours) Actual outbreaks Actual outbreaks Linear (Actual outbreaks)  98  Since the infection risk is expected to be zero at time 0, the trend line is forced to pass (0,0). As shown in the figure, the infection risk, P, can be expressed as P=0.043t, where t is the exposure time. By using this linear relationship to calculate the pathogen concentration in the respiratory fluid while cough frequency, particle volume and pulmonary rate change, the optimal parameter set can be determined. Table F-2 Cases summary of optimal parameter set selection Case ID cough frequency particle volume pulmonary rate pathogen concentration (times/hour) (m3/hour) (mL-1) 1 3 Duguid1 0.9 1.01E+09 2 3 LR2 0.9 1.14E+09 3 3 Chao3 0.9 2.21E+09 4 3 Zhu4 0.9 1.95E+09 5 3 Duguid 1.8 5.06E+08 6 3 LR 1.8 5.69E+08 7 3 Chao 1.8 1.11E+09 8 3 Zhu 1.8 9.73E+08 9 12 Duguid 0.9 2.55E+08 10 12 LR 0.9 2.87E+08 11 12 Chao 0.9 5.58E+08 12 12 Zhu 0.9 4.90E+08 13 12 Duguid 1.8 1.28E+08 14 12 LR 1.8 1.44E+08 15 12 Chao 1.8 2.79E+08 16 12 Zhu 1.8 2.45E+08 Notes: 1. (Duguid, 1946) 2. (Nicas, Nazaroff, & Hubbard, 2005) 3. (Chao, et al., 2009) 4. (Zhu, Kato, & Yang, 2006)  The virus concentration in respiratory fluid is about 7x104pfu/ml (Sze To, et al., 2008).As shown in Table 2, Case 13 is the closest parameter set. However, the published concentration is  99  significantly smaller than the estimated value, which has the difference of four order of magnitude. This difference could be caused by inaccuracy of the published virus concentration value or uncertainty of the three actual outbreak cases used here. For example, if the actual cases happened under extreme conditions, the trend line shown in Figure F-1 could have a huge variation against correct value. To improve reliability of this model, more influenza outbreak cases are desired to be collected as reference.  Viability-Influenza Several studies conducted experiments in laboratory and develop mathematical models to simulate the behavior of pathogen of influenza in different environmental conditions. Its viability has also been illustrated in those research. According to Hemmes (Hemmes, Winkler, & Kool, 1962), under 20oC and 60% RH, about 20% virus remains viable at time 0. In 2009, Posada developed a mathematical model, using water activity as the independent variable, to predict the viability of airborne viruses under different relative humidity conditions. Posada proposed an empirical exponential decay function by fitting the published experimental data conducted by Schaffer on influenza A, as shown below: ܵ = ߙ݁ିఉ௧೙                                                                    (F-1) Where ܵ  is viability of infective airborne viruses; ߙ  and ߚ  are model coefficients; ݐ  is the exposure time; ݊ controls the viability decay rate. ߚ = ܿଵe[ି௖మ(௔ೢି௔೎ೝ)మ] + ܿଷܽ௪௤                                                       (F-2) Where ܿଵ, ܿଶ, ܿଷand ݍ are model coefficients; ܽ௪ is water activity in the solution, i.e. the vapor pressure of water in a solution divided by the saturation vapor pressure of pure water under the same condition; ܽ௥ is the critical water activity.  100  According to Posada, the overall viability decay for influenza A is described as follows: ܵ = 0.13݁ି଴.଴଼ଶହ௧బ.ఱ                                                             (F-3) To gain a better understanding of this property of pathogen, based on the Posada’s research, the following figure indicates the viability of influenza at relative humidity at 45%. (Posada, Redrow, & Celik, 2010)  Figure F-2 Viability of Influenza at RH 45% Posada's research is based on Schaffer’s experimental data. In this study, Schaffer started the experiment focusing on the recovery rate of influenza A virus under different relative humidity. The effectiveness of various host cell culture is then determined in terms of viability decay. Specifically, Schaffer conducted this experiment in a 208-L stirred settling chamber with a Wells refluxing atomizer at 21oC. According to Schaffer, RH and spray medium were the most profound factors to viability of airborne viruses among other environmental conditions. (Schaffer, Scergel, & Straube , 1976) As shown in the above figure, the viability decays from approximately 13% to 1% within one hour. Due to the rapidly drying and aerosolization of the  101  airborne droplets at the first one to two minutes (Schaffer, Scergel, & Straube , 1976), Schaffer concluded that the viability would experience a significant loss. By applying back extrapolation, the initial viability was determined by “secondary survival” rate, which is defined from 15 to 60 minutes. Thus, as shown in the figure above, the initial viability, approximately at 13%, was the viability at one minute respective. The original viability was at 100% at time zero.                102  Appendix G: Cough frequency studies In this paper, two cough frequencies are selected as the model inputs, three times per hour (Loudon & Roberts, 1967) and twelve times per hour (Hsu, Stone, Logan-Sinclair, Worsdell, Busst , & Chung, 1994). According to Loudon, more than half of 96 TB patients coughed three times per hour during the data recording period. The extreme record was 48 times per hour. Based on Hsu's research, asthmatic patients coughed about twelve times per hour during 24 hours of exposure. As a key parameter in this model, cough frequency has profound impact on the overall pathogen generation rate. The cough frequency are independently depends on case and disease. To estimate a more reasonable value for cough frequency, research was carried out for different diseases. The purpose of doing this appendix is to establish a cough frequency database for different diseases; therefore the model can be applied to various airborne or similar symptom diseases. There are three other cough frequency studies. 1. S. S. Birring, et al. (2005), Cough frequency, cough sensitivity and health status in patients with chronic cough, Respiratory Medicine, 100: 1105-1109 • Description:  In this paper, Leicester Cough Monitor (LCM) is used to measure the cough times.  LCM monitors the sound generated by coughing only. Six hours is set as the testing  period. • Results: a) Twenty patients with chronic cough disease:  The mean (SEM) is 43 (8) coughs/hour  (SEM: standard error of mean: the spread that  the mean of a sample of values would have if keep taking samples)  103  b) Nine healthy subjects:   The mean (SEM) is 2 (1) coughs/hour  2. M. Paul, et al. (2006),  Evaluation of a new self-contained, ambulatory, objective cough monitor, Cough, 2:7, 1745-1786 • Description:  Fifteen subjects with frequent coughing performed the test. The data recording time was  ranged from 15 to 60 minutes. The subjects' age were from 2 weeks to 80 years old. • Results:  The average video counts and monitor counts were 44 times/hour and 42 times/hour,  respectively.  3. J. J. Kuhn, et al. (1982),  Antitussive effect of guaifenesin in young adults with natural colds,   American College of Chest Physicians, 82: 713-718 • Description:         Forty-two patients performed the test with 24 hours exposure. The patients had acute respiratory illness • Results:  For a six hours interval, the cough median was from 17 to 210 for the vehicle group; for  guaifensin group, it was from 12 to 377.   104  Appendix H: Particle distribution The original particle distributions (un-weighted) are plotted as follows:    1.E-17 1.E-16 1.E-15 1.E-14 1.E-13 1.E-12 1.E-11 1.E-10 1.E-09 1.E-08 1.E-07 1 10 100 1000 10000 d V / d ln D p Diameter (µm) Original Volume Distribution LR (1967) Duguid (1946) Zhu (2006) Chao (2009) CFD data

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