Estimation of Tuberculosis Risk on a Commercial Airliner

This article estimates the risk of tuberculosis (TB) transmission on a typical commercial airliner using a simple one box model (OBM) and a sequential box model (SBM). We used input data derived from an actual TB exposure on an airliner, and we assumed a hypothetical scenario that a highly infectious TB source case (i.e., 108 infectious quanta per hour) travels as a passenger on an 8.7-hour flight. We estimate an average risk of TB transmission on the order of 1 chance in 1,000 for all passengers using the OBM. Applying the more realistic SBM, we show that the risk and incidence decrease sharply in a stepwise fashion in cabins downstream from the cabin containing the source case assuming some potential for airflow from more contaminated to less contaminated cabins. We further characterized spatial variability in the risk within the cabin by modeling a previously reported TB outbreak in an airplane to demonstrate that the TB cases occur most likely within close proximity of the source TB patient.     

A Simulation Model for Occupational Tuberculosis Transmission

A simulation model of tuberculosis (TB) transmission among hospital employees is described. A hypothetical cohort of 1000 workers was divided into low-, medium-, and high-risk groups. The number of TB patients admitted daily was treated as a Poisson random variable. A patient imparted a daily infection risk that was identical for all workers within a risk group but that varied between risk groups. In some scenarios, infected employees were assigned a daily risk of developing TB disease. If disease developed, the individual remained on the job for 3 calendar weeks and imparted a substantial infection risk to 25 close contacts. Simulations were run over 5-year intervals. Cumulative infection incidence increased over time and with more TB patients admitted. Given a scenario in which there were 600, 300, and 100 susceptibles in the low-, medium-, and high risk groups, respectively, 50 TB patients admitted annually and accounting for disease among infected employees, at 5 years there were approximately 100 primary infections (due to infection by patients), 40 secondary infections (due to infection by diseased coworkers), five primary disease cases, and two secondary disease cases. The input parameter values and simulation outcomes were reasonably consistent with the sparse information reported in the literature.     

An Integrated Model of Infection Risk in a Health-Care Environment

Certain respiratory tract infections can be transmitted by hand-to-mucous-membrane contact, inhalation, and/or direct respiratory droplet spray. In a room occupied by a patient with such a transmissible infection, pathogens present on textile and nontextile surfaces, and pathogens present in the air, provide sources of exposure for an attending health-care worker (HCW); in addition, close contact with the patient when the latter coughs allows for droplet spray exposure. We present an integrated model of pertinent source-environment-receptor pathways, and represent physical elements in these pathways as "states" in a discrete-time Markov chain model. We estimate the rates of transfer at various steps in the pathways, and their relationship to the probability that a pathogen in one state has moved to another state by the end of a specified time interval. Given initial pathogen loads on textile and nontextile surfaces and in room air, we use the model to estimate the expected pathogen dose to a HCW's mucous membranes and respiratory tract. In turn, using a nonthreshold infectious dose model, we relate the expected dose to infection risk. The system is illustrated with a hypothetical but plausible scenario involving a viral pathogen emitted via coughing. We also use the model to show that a biocidal finish on textile surfaces has the potential to substantially reduce infection risk via the hand-to-mucous-membrane exposure pathway.     

Characterizing the Risk of Infection from Mycobacterium tuberculosis in Commercial Passenger Aircraft Using Quantitative Microbial Risk Assessment

Quantitative microbial risk assessment was used to predict the likelihood and spatial organization of Mycobacterium tuberculosis ( Mtb ) transmission in a commercial aircraft. Passenger exposure was predicted via a multizone Markov model in four scenarios: seated or moving infectious passengers and with or without filtration of recirculated cabin air. The traditional exponential ( k  = 1) and a new exponential ( k  = 0.0218) dose-response function were used to compute infection risk. Emission variability was included by Monte Carlo simulation. Infection risks were higher nearer and aft of the source; steady state airborne concentration levels were not attained. Expected incidence was low to moderate, with the central 95% ranging from 10⁻⁶ to 10⁻¹ per 169 passengers in the four scenarios. Emission rates used were low compared to measurements from active TB patients in wards, thus a "superspreader" emitting 44 quanta/h could produce 6.2 cases or more under these scenarios. Use of respiratory protection by the infectious source and/or susceptible passengers reduced infection incidence up to one order of magnitude.     

A Probabilistic Transmission Dynamic Model to Assess Indoor Airborne Infection Risks

The purpose of this article is to quantify the public health risk associated with inhalation of indoor airborne infection based on a probabilistic transmission dynamic modeling approach. We used the Wells-Riley mathematical model to estimate (1) the CO2 exposure concentrations in indoor environments where cases of inhalation airborne infection occurred based on reported epidemiological data and epidemic curves for influenza and severe acute respiratory syndrome (SARS), (2) the basic reproductive number, R0 (i.e., expected number of secondary cases on the introduction of a single infected individual in a completely susceptible population) and its variability in a shared indoor airspace, and (3) the risk for infection in various scenarios of exposure in a susceptible population for a range of R0. We also employ a standard susceptible-infectious-recovered (SIR) structure to relate Wells-Riley model derived R0 to a transmission parameter to implicate the relationships between indoor carbon dioxide concentration and contact rate. We estimate that a single case of SARS will infect 2.6 secondary cases on average in a population from nosocomial transmission, whereas less than 1 secondary infection was generated per case among school children. We also obtained an estimate of the basic reproductive number for influenza in a commercial airliner: the median value is 10.4. We suggest that improving the building air cleaning rate to lower the critical rebreathed fraction of indoor air can decrease transmission rate. Here, we show that virulence of the organism factors, infectious quantum generation rates (quanta/s by an infected person), and host factors determine the risk for inhalation of indoor airborne infection.     

A Probabilistic Transmission Model to Assess Infection Risk from Mycobacterium Tuberculosis in Commercial Passenger Trains

The objective of this article is to characterize the risk of infection from airborne Mycobacterium tuberculosis bacilli exposure in commercial passenger trains based on a risk‐based probabilistic transmission modeling. We investigated the tuberculosis (TB) infection risks among commercial passengers by inhaled aerosol M. tuberculosis bacilli and quantify the patterns of TB transmission in Taiwan High Speed Rail (THSR). A deterministic Wells‐Riley mathematical model was used to account for the probability of infection risk from M. tuberculosis bacilli by linking the cough‐generated aerosol M. tuberculosis bacilli concentration and particle size distribution. We found that (i) the quantum generation rate of TB was estimated with a lognormal distribution of geometric mean (GM) of 54.29 and geometric standard deviation (GSD) of 3.05 quantum/h at particle size ≤ 5 μm and (ii) the basic reproduction numbers (R₀) were estimated to be 0.69 (0.06–6.79), 2.82 (0.32–20.97), and 2.31 (0.25–17.69) for business, standard, and nonreserved cabins, respectively. The results indicate that commercial passengers taking standard and nonreserved cabins had higher transmission risk than those in business cabins based on conservatism. Our results also reveal that even a brief exposure, as in the bronchoscopy cases, can also result in a transmission when the quantum generation rate is high. This study could contribute to a better understanding of the dynamics of TB transmission in commercial passenger trains by assessing the relationship between TB infectiousness, passenger mobility, and key model parameters such as seat occupancy, ventilation rate, and exposure duration.     

A probabilistic transmission and population dynamic model to assess tuberculosis infection risk

The purpose of this study was to examine tuberculosis (TB) population dynamics and to assess potential infection risk in Taiwan. A well‐established mathematical model of TB transmission built on previous models was adopted to study the potential impact of TB transmission. A probabilistic risk model was also developed to estimate site‐specific risks of developing disease soon after recent primary infection, exogenous reinfection, or through endogenous reactivation (latently infected TB) among Taiwan regions. Here, we showed that the proportion of endogenous reactivation (53–67%) was larger than that of exogenous reinfection (32–47%). Our simulations showed that as epidemic reaches a steady state, age distribution of cases would finally shift toward older age groups dominated by latently infected TB cases as a result of endogenous reactivation. A comparison of age‐weighted TB incidence data with our model simulation output with 95% credible intervals revealed that the predictions were in an apparent agreement with observed data. The median value of overall basic reproduction number (R₀) in eastern Taiwan ranged from 1.65 to 1.72, whereas northern Taiwan had the lowest R₀ estimate of 1.50. We found that total TB incidences in eastern Taiwan had 25–27% probabilities of total proportion of infected population exceeding 90%, whereas there were 36–66% probabilities having exceeded 20% of total proportion of infected population attributed to latently infected TB. We suggested that our Taiwan‐based analysis can be extended to the context of developing countries, where TB remains a substantial cause of elderly morbidity and mortality.     

Modeling the Airborne Infection Risk of Tuberculosis for a Research Facility in eMalahleni,South Africa

A detailed mathematical modeling framework for the risk of airborne infectious disease transmission in indoor spaces was developed to enable mathematical analysis of experiments conducted at the Airborne Infections Research (AIR) facility, eMalahleni, South Africa. A model was built using this framework to explore possible causes of why an experiment at the AIR facility did not produce expected results. The experiment was conducted at the AIR facility from August 31, 2015 to December 4, 2015, in which the efficacy of upper room germicidal ultraviolet (GUV) irradiation as an environmental control was tested. However, the experiment did not produce the expected outcome of having fewer infections in the test animal room than the control room. The simulation results indicate that dynamic effects, caused by switching the GUV lights, power outages, or introduction of new patients, did not result in the unexpected outcomes. However, a sensitivity analysis highlights that significant uncertainty exists with risk of transmission predictions based on current measurement practices, due to the reliance on large viable literature ranges for parameters.     

All the bottles in one basket? Evaluating the effect of intra-industry diversification on risk

This paper develops a framework using Monte Carlo simulation to examine risk/return properties of intra-industry product portfolio composition and diversification. We use product-level data covering all Swedish sales of alcoholic beverages to describe the risk profiles of wholesalers and how they are affected by actual and hypothetical changes to product portfolios. Using a large number of counterfactual portfolios we quantify the diversification benefits of different product portfolio compositions. In this market the most important reductions in variability come from focusing on domestic products and from focusing on product categories that have low variability. The number of products also has a large effect in the simulations, moving from a portfolio of 10 products to one of 20 products cuts standard deviation of cash flows in relation to mean cash flows by more than half. The concentration of import origins plays a minor quantitative role on risk/return profiles in this market.     

A Case Study Evaluating the Risk of Infection from Middle Eastern Respiratory Syndrome Coronavirus (MERS‐CoV) in a Hospital Setting Through Bioaerosols

Middle Eastern respiratory syndrome, an emerging viral infection with a global case fatality rate of 35.5%, caused major outbreaks first in 2012 and 2015, though new cases are continuously reported around the world. Transmission is believed to mainly occur in healthcare settings through aerosolized particles. This study uses Quantitative Microbial Risk Assessment to develop a generalizable model that can assist with interpreting reported outbreak data or predict risk of infection with or without the recommended strategies. The exposure scenario includes a single index patient emitting virus‐containing aerosols into the air by coughing, leading to short‐ and long‐range airborne exposures for other patients in the same room, nurses, healthcare workers, and family visitors. Aerosol transport modeling was coupled with Monte Carlo simulation to evaluate the risk of MERS illness for the exposed population. Results from a typical scenario show the daily mean risk of infection to be the highest for the nurses and healthcare workers (8.49 × 10^?4 and 7.91 × 10^?4, respectively), and the lowest for family visitors and patients staying in the same room (3.12 × 10^?4 and 1.29 × 10^?4, respectively). Sensitivity analysis indicates that more than 90% of the uncertainty in the risk characterization is due to the viral concentration in saliva. Assessment of risk interventions showed that respiratory masks were found to have a greater effect in reducing the risks for all the groups evaluated (>90% risk reduction), while increasing the air exchange was effective for the other patients in the same room only (up to 58% risk reduction).     

Structure and Parameterization of Pharmacokinetic Models: Their Impact on Model Predictions

There has been an increasing interest in physiologically based pharmacokinetic (PBPK)models in the area of risk assessment. The use of these models raises two important issues: (1)How good are PBPK models for predicting experimental kinetic data? (2)How is the variability in the model output affected by the number of parameters and the structure of the model? To examine these issues, we compared a five-compartment PBPK model, a three-compartment PBPK model, and nonphysiological compartmental models of benzene pharmacokinetics. Monte Carlo simulations were used to take into account the variability of the parameters. The models were fitted to three sets of experimental data and a hypothetical experiment was simulated with each model to provide a uniform basis for comparison. Two main results are presented: (1)the difference is larger between the predictions of the same model fitted to different data se1ts than between the predictions of different models fitted to the dame data; and (2)the type of data used to fit the model has a larger effect on the variability of the predictions than the type of model and the number of parameters.     

Framework for Microbial Food‐Safety Risk Assessments Amenable to Bayesian Modeling

Regulatory agencies often perform microbial risk assessments to evaluate the change in the number of human illnesses as the result of a new policy that reduces the level of contamination in the food supply. These agencies generally have regulatory authority over the production and retail sectors of the farm‐to‐table continuum. Any predicted change in contamination that results from new policy that regulates production practices occurs many steps prior to consumption of the product. This study proposes a framework for conducting microbial food‐safety risk assessments; this framework can be used to quantitatively assess the annual effects of national regulatory policies. Advantages of the framework are that estimates of human illnesses are consistent with national disease surveillance data (which are usually summarized on an annual basis) and some of the modeling steps that occur between production and consumption can be collapsed or eliminated. The framework leads to probabilistic models that include uncertainty and variability in critical input parameters; these models can be solved using a number of different Bayesian methods. The Bayesian synthesis method performs well for this application and generates posterior distributions of parameters that are relevant to assessing the effect of implementing a new policy. An example, based on Campylobacter and chicken, estimates the annual number of illnesses avoided by a hypothetical policy; this output could be used to assess the economic benefits of a new policy. Empirical validation of the policy effect is also examined by estimating the annual change in the numbers of illnesses observed via disease surveillance systems.     

Probability of Exporting Infected Carcasses from Vaccinated Pigs Following a Foot‐and‐Mouth Disease Epidemic

Emergency vaccination is an effective control strategy for foot‐and‐mouth disease (FMD) epidemics in densely populated livestock areas, but results in a six‐month waiting period before exports can be resumed, incurring severe economic consequences for pig exporting countries. In the European Union, a one‐month waiting period has been discussed based on negative test results in a final screening. The objective of this study was to analyze the risk of exporting FMD‐infected pig carcasses from a vaccinated area: (1) directly after final screening and (2) after a six‐month waiting period. A risk model has been developed to estimate the probability that a processed carcass was derived from an FMD‐infected pig (P_carc). Key variables were herd prevalence (P_H), within‐herd prevalence (P_A), and the probability of detection at slaughter (P_SL). P_H and P_A were estimated using Bayesian inference under the assumption that, despite all negative test results, ≥1 infected pigs were present. Model calculations indicated that P_carc was on average 2.0 × 10^?5 directly after final screening, and 1.7 × 10^?5 after a six‐month waiting period. Therefore, the additional waiting time did not substantially reduce P_carc. The estimated values were worst‐case scenarios because only viraemic pigs pose a risk for disease transmission, while seropositive pigs do not. The risk of exporting FMD via pig carcasses from a vaccinated area can further be reduced by heat treatment of pork and/or by excluding high‐risk pork products from export.     

Tracking national and regional spatial-temporal mortality risk associated with NO2 concentrations in Canada: a Bayesian hierarchical two-level model

The association between daily variations in urban air quality and mortality has been well documented using time series statistical methods. This approach assumes a constant association over time. We develop a space-time dynamic model that relaxes this assumption, thus more directly examining the hypothesis that improvements in air quality translate into improvements in public health. We postulate a Bayesian hierarchical two-level model to estimate annual mortality risks at regional and national levels and to track both risk and heterogeneity of risk within and between regions over time. We illustrate our methods using daily nitrogen dioxide concentrations (NO2) and nonaccidental mortality data collected for 1984-2004 in 24 Canadian cities. Estimates of risk and heterogeneity are compared by cause of mortality (cardio-pulmonary [CP] versus non-CP) and season, respectively. Over the entire period, the NO2 risk for CP mortality was slightly lower but with a narrower credible interval than that for non-CP mortality, mainly due to an unusually low risk for a single year (1998). Warm season NO2 risk was higher than cold season risk for both CP and non-CP mortality. For 21 years overall there were no significant differences detected among the four regional NO2 risks. We found overall that there was no strong evidence for time trends in NO2 risk at national or regional levels. However, an increasing linear time trend in the annual between-region heterogeneities was detected, which suggests the differences in risk among the four regions are getting larger, and further studies are necessary to understand the increasing heterogeneity.     

Uncertainty Assessment in the Quantification of Risk Rates of Occupational Accidents

Occupational risk rates per hour of exposure have been quantified for 63 occupational accident types for the Dutch working population. Data were obtained from the analysis of more than 9,000 accidents that occurred over a period of six years in the Netherlands and resulted in three types of reportable consequences under Dutch law: (a) fatal injury, (b) permanent injury, and (c) serious recoverable injury requiring at least one day of hospitalization. A Bayesian uncertainty assessment on the value of the risk rates has been performed. Annual risks for each of the 63 occupational accident types have been calculated, including the variability in the annual exposure of the working population to the corresponding hazards. The suitability of three risk measures—individual risk rates, individual annual risk, and number of accidents—is examined and discussed.     

Environmental Surveillance System Characteristics and Impacts on Confidence About No Undetected Serotype 1 Wild Poliovirus Circulation

Surveillance for poliovirus during the polio endgame remains uncertain. Building on prior modeling of the potential for undetected poliovirus transmission for conditions like those in Pakistan and Afghanistan, we use a hypothetical model to explore several key characteristics of the poliovirus environmental surveillance (ES) system (e.g., number and quality of sites, catchment sizes, and sampling frequency) and characterize their impacts on the time required to reach high (i.e., 95%) confidence about no circulation (CNC95%) following the last detected case of serotype 1 wild poliovirus. The nature and quality of the existing and future acute flaccid paralysis (AFP) surveillance and ES system significantly impact the estimated CNC95% for places like Pakistan and Afghanistan. The analysis illustrates the tradeoffs between number of sites, sampling frequency, and catchments sizes, and suggests diminishing returns of increasing these three factors beyond a point that depends on site quality and the location of sites. Limitations in data quality and the hypothetical nature of the model reduce the ability to assess the extent to which actual ES systems offer benefits that exceed their costs. Thus, although poliovirus ES may help to reduce the time required to reach high confidence about the absence of undetected circulation, the effect strongly depends on the ability to establish effective ES sites in high‐risk areas. The costs and benefits of ES require further analysis.     

A Model for Planning Resource Requirements in Health Care Organizations

In this paper we present a general model and solution methodology for planning resource requirements (i.e., capacity) in health care organizations. To illustrate the general model, we consider two specific applications: a blood bank and a health maintenance organization (HMO). The blood bank capacity planning problem involves determining the number of donor beds required and determining the size of the nursing and support staff necessary. Capacity must be sufficient to handle the expected number of blood donors without causing excessive donor waiting times. Similar staff, equipment, and service level decisions arise in the HMO capacity planning problem. To determine resource requirements, we develop an optimization/queueing network model that minimizes capacity costs while controlling customer service by enforcing a set of performance constraints, such as setting an upper limit on the expected time a patient spends in the system. The queueing network model allows us to capture the stochastic behavior of health care systems and to measure customer service levels within the optimization framework.     

APPROXIMATIONS FOR THE GI/G/m QUEUE

Queueing models can usefully represent production systems experiencing congestion due to irregular flows, but exact analyses of these queueing models can be difficult. Thus it is natural to seek relatively simple approximations that are suitably accurate for engineering purposes. Here approximations for a basic queueing model are developed and evaluated. The model is the GI/G/m queue, which has m identical servers in parallel, unlimited waiting room, and the first-come first-served queue discipline, with service and interarrival times coming from independent sequences of independent and identically distributed random variables with general distributions. The approximations depend on the general interarrival-time and service-time distributions only through their first two moments. The main focus is on the expected waiting time and the probability of having to wait before beginning service, but approximations are also developed for other congestion measures, including the entire distributions of waiting time, queue-length and number in system. These relatively simple approximations are useful supplements to algorithms for computing the exact values that have been developed in recent years. The simple approximations can serve as starting points for developing approximations for more complicated systems for which exact solutions are not yet available. These approximations are especially useful for incorporating GI/G/m models in larger models, such as queueing networks, wherein the approximations can be components of rapid modeling tools.     

Risk Assessment of Human Toxoplasmosis Associated with the Consumption of Pork Meat in Italy

Toxoplasmosis is a cosmopolitan disease and has a broad range of hosts, including humans and several wild and domestic animals. The human infection is mostly acquired through the consumption of contaminated food and pork meat has been recognized as one of the major sources of transmission. There are, however, certain fundamental differences between countries; therefore, the present study specifically aims to evaluate the exposure of the Italian population to Toxoplasma gondii through the ingestion of several types of pork meat products habitually consumed in Italy and to estimate the annual number of human infections within two subgroups of the population. A quantitative risk assessment model was built for this reason and was enriched with new elements in comparison to other similar risk assessments in order to enhance its accuracy. Sensitivity analysis and two alternative scenarios were implemented to identify the factors that have the highest impact on risk and to simulate different plausible conditions, respectively. The estimated overall average number of new infections per year among adults is 12,513 and 92 for pregnant women. The baseline model showed that almost all these infections are associated with the consumption of fresh meat cuts and preparations (mean risk of infection varied between 4.5 × 10⁻⁵ and 5.5 × 10⁻⁵) and only a small percentage is due to fermented sausages/salami. On the contrary, salt‐cured meat products seem to pose minor risk but further investigations are needed to clarify still unclear aspects. Among all the considered variables, cooking temperature and bradyzoites’ concentration in muscle impacted most the risk.     

A Trichloroethylene Risk Assessment Using a Monte Carlo Analysis of Parameter Uncertainty in Conjunction with Physiologically-Based Pharmacokinetic Modeling

A Monte Carlo simulation is incorporated into a risk assessment for trichloroethylene (TCE) using physiologically-based pharmacokinetic (PBPK) modeling coupled with the linearized multistage model to derive human carcinogenic risk extrapolations. The Monte Carlo technique incorporates physiological parameter variability to produce a statistically derived range of risk estimates which quantifies specific uncertainties associated with PBPK risk assessment approaches. Both inhalation and ingestion exposure routes are addressed. Simulated exposure scenarios were consistent with those used by the Environmental Protection Agency (EPA) in their TCE risk assessment. Mean values of physiological parameters were gathered from the literature for both mice (carcinogenic bioassay subjects) and for humans. Realistic physiological value distributions were assumed using existing data on variability. Mouse cancer bioassay data were correlated to total TCE metabolized and area-under-the-curve (blood concentration) trichloroacetic acid (TCA) as determined by a mouse PBPK model. These internal dose metrics were used in a linearized multistage model analysis to determine dose metric values corresponding to 10^-6 lifetime excess cancer risk. Using a human PBPK model, these metabolized doses were then extrapolated to equivalent human exposures (inhalation and ingestion). The Monte Carlo iterations with varying mouse and human physiological parameters produced a range of human exposure concentrations producing a 10^-6 risk.