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.     

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.     

Estimation of Tuberculosis Risk and Incidence under Upper Room Ultraviolet Germicidal Irradiation in a Waiting Room in a Hypothetical Scenario

Environmental control measures (ventilation, high-efficiency particulate air filtration, and upper room ultraviolet germicidal irradiation [UVGI]) are recommended to effectively control tuberculosis (TB) transmission from unsuspected TB patients in high-risk settings, but the effectiveness of their use is not often clear. This study presents a simulation model for a hypothetical hospital waiting room, in which the number of susceptible immunocompetent people in the waiting room follows a Poisson distribution (M = 5) in either low (annual number of TB patients = 5) or high TB risk settings (annual number of TB patients = 50), and used the model to evaluate the reduction of TB transmission risk by upper room UVGI. An exponential dose-response model was used for TB transmission and a two-zone model was used for evaluating the effect of upper room UVGI. Upper room UVGI reduced TB risk by 1.6-fold at 3 microW/cm2 UV irradiance in the upper room in the low TB risk setting and by 4.1-fold at 15 microW/cm2 UV irradiance in the upper room in the high TB risk setting. Use of upper room UVGI also reduced the mean annual new infection rate from 2.2 to 1.3 infections per year at 3 microW/cm2 and to 0.6 infections per year at 15 microW/cm2 in our hypothetical high-risk settings. The effect of upper room UVGI was sensitive to both vertical air velocity (air mixing) and UV irradiance level. Results from partitioning variability indicate that most variability of TB transmission risk came from waiting time in our hypothetical hospital.     

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.     

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.     

Collaborative optimization for metro train scheduling and train connections combined with passenger flow control strategy

For high-frequency metro lines, the excessive travel demand during the peak hours brings a high risk to metro system and a low comfort to passengers, so it is important to consider passenger flow control when designing the metro train scheduling strategy. This paper presents a collaborative optimization method for metro train scheduling and train connections combined with passenger control strategy on a bi-directional metro line. Specifically, the dynamic equations for the train headway and train passenger loads along the metro line, the turnaround operations and the entering/exiting depot operations are considered simultaneously. The proposed collaborative optimization problem is formulated as a mixed integer nonlinear programming model to realise the trade-off among the utilization of trains, passenger flow control strategy and the number of awaiting passengers at platforms, which is further reformulated into mixed integer linear programming (MILP) model. To handle the complexity of this MILP model, a Lagrangian relaxation-based approach is designed to decompose the original problem into two small subproblems, which reduces the computational burden of the original problem and can efficiently find a good solution of the train schedule and train connections problem combined with passenger flow control strategy. The numerical experiments are implemented to investigate the effectiveness of the proposed model and approach, which shows that the proposed model is not sensitive to uncertain passenger demand. Under the proposed collaborative optimization approach, the number of train service connections and the crowding inside stations and carriages with the proper passenger flow control strategy can be evidently balanced, and thereby the operation efficiency and safety of the metro lines are effectively improved.     

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.     

Recoverable robust timetabling for single delay: Complexity and polynomial algorithms for special cases

In this paper, we study the problem of planning a timetable for passenger trains considering that possible delays might occur due to unpredictable circumstances. If a delay occurs, a timetable could not be able to manage it unless some extra time has been scheduled in advance. Delays might be managed in several ways and the usual objective function considered for such purpose is the minimization of the overall waiting time caused to passengers. We analyze the timetable planning problem in terms of the recoverable robustness model, where a timetable is said to be recoverable robust if it is able to absorb small delays by possibly applying given limited recovery capabilities. The quality of a robust timetable is measured by the price of robustness that is the ratio between the cost of the recoverable robust timetable and that of a non-robust optimal one.     

Modeling exotic highly pathogenic avian influenza virus entrance risk through air passenger violations

The highly pathogenic avian influenza virus (HPAIV) is able to survive in poultry products and could be carried into a country by air travelers. An assessment model was constructed to estimate the probability of the exotic viable HPAIV entering Taiwan from two neighboring areas through poultry products carried illegally by air passengers at Taiwan's main airports. The entrance risk was evaluated based on HPAIV-related factors (the prevalence and the incubation period of HPAIV; the manufacturing process of poultry products; and the distribution-storage-transportation factor event) and the passenger event. Distribution functions were adopted to simulate the probabilities of each HPAIV factor. The odds of passengers being intercepted with illegal poultry products were estimated by logistic regression. The Monte Carlo simulation established that the risk caused by HPAIV-related factors from area A was lower than area B, whereas the entrance risk by the passenger event from area A was similar to area B. Sensitivity analysis showed that the incubation period of HPAIV and the interception of passenger violations were major determinants. Although the result showed viable HPAIV was unlikely to enter Taiwan through meat illegally carried by air passengers, this low probability could be caused by incomplete animal disease data and modeling uncertainties. Considering the negative socioeconomic impacts of HPAIV outbreaks, strengthening airport quarantine measures is still necessary. This assessment provides a profile of HPAIV entrance risk through air travelers arriving from endemic areas and a feasible direction for quarantine and public health measures.     

An Analytical Framework for Relating Dose, Risk, and Incidence: An Application to Occupational Tuberculosis Infection

An adverse health impact is often treated as a binary variable (response vs. no response), in which case the risk of response is defined as a monotonically increasing function R of the dose received D. For a population of size N , specifying the forms of R(D) and of the probability density function (pdf) for D allows determination of the pdf for risk, and computation of the mean and variance of the distribution of incidence, where the latter parameters are denoted E[S _N] and Var[ S _N], respectively. The distribution of S _N describes uncertainty in the future incidence value. Given variability in dose (and risk) among population members, the distribution of incidence is Poisson-binomial. However, depending on the value of E[S _N], the distribution of incidence is adequately approximated by a Poisson distribution with parameter μ= E[S _N], or by a normal distribution with mean and variance equal to E[S _N] and Var[ S _N]. The general analytical framework is applied to occupational infection by Mycobacterium tuberculosis (M. tb). Tuberculosis is transmitted by inhalation of 1–5 μm particles carrying viable M. tb bacilli. Infection risk has traditionally been modeled by the expression: R(D) = 1 – exp(– D ), where D is the expected number of bacilli that deposit in the pulmonary region. This model assumes that the infectious dose is one bacillus. The beta pdf and the gamma pdf are shown to be reasonable and especially convenient forms for modeling the distribution of the expected cumulative dose across a large healthcare worker cohort. Use of the the analytical framework is illustrated by estimating the efficacy of different respiratory protective devices in reducing healthcare worker infection risk.     

COVID-19疫情下一种新的地铁平峰运营策略

地铁在城市交通中发挥着重要作用。然而，在新冠肺炎(COVID-19)疫情下，地铁的运营出现了包括消毒、限流及出行独立等多重约束。错峰出行成为了众多城市地铁运营过程中的必然选择。如何既满足居民的基本出行需求，为顺利实现复工复学提供交通支持，又能有效降低乘客感染病毒的风险与追踪密切接触者的成本成为了城市地铁运营的新目标。本文通过对北京地铁运营现状及居民的出行规律分析发现，在新型冠状病毒疫情下，地铁运营过程中存在出行需求与地铁运力不匹配，复工复产与疫情防控，乘客交叉出行数量过多等难题，并针对以上难题提出了分时段复工出行与周末可复工在内的复杂指派模型。这一指派模型不仅实现了城市关键地铁站点平峰人流量、降低疫情传播风险及追踪难度的目标，同时通过模型目标函数与约束条件的灵活修改可实现更为复杂的乘坐地铁复工复产目标。本文所提出的模型在复杂周期性平峰问题中具有较强的推广应用价值。     

Quelling Cabin Noise in Turboprop Aircraft via Active Control

Cabin noise in turboprop aircraft causes passenger discomfort, airframe fatigue, and employee scheduling constraints due to OSHA standards for exposure to high levels of noise. The noise levels in the cabins of turboprop aircraft are typically 10 to 30 decibels louder than commercial jet noise levels. However, unlike jet noise the turboprop noise spectrum is dominated by a few low frequency tones. Active structural acoustic control is a method in which the control inputs (used to reduce interior noise) are applied directly to a vibrating structural acoustic system. The control concept modeled in this work is the application of in-plane force inputs to piezoceramic patches bonded to the wall of a vibrating cylinder. The goal is to determine the force inputs and locations for the piezoceramic actuators so that (1) the interior noise is effectively damped; (2) the level of vibration of the cylinder shell is not increased; and (3) the power requirements needed to drive the actuators are not excessive. Computational experiments for data taken from a computer generated model and from a laboratory test article at NASA Langley Research Center are provided.     

Risk‐Based Decision Making for Reoccupation of Contaminated Areas Following a Wide‐Area Anthrax Release

This article presents an analysis of postattack response strategies to mitigate the risks of reoccupying contaminated areas following a release of Bacillus anthracis spores (the bacterium responsible for causing anthrax) in an urban setting. The analysis is based on a hypothetical attack scenario in which individuals are exposed to B. anthracis spores during an initial aerosol release and then placed on prophylactic antibiotics that successfully protect them against the initial aerosol exposure. The risk from reoccupying buildings contaminated with spores due to their reaerosolization and inhalation is then evaluated. The response options considered include: decontamination of the buildings, vaccination of individuals reoccupying the buildings, extended evacuation of individuals from the contaminated buildings, and combinations of these options. The study uses a decision tree to estimate the costs and benefits of alternative response strategies across a range of exposure risks. Results for best estimates of model inputs suggest that the most cost‐effective response for high‐risk scenarios (individual chance of infection exceeding 11%) consists of evacuation and building decontamination. For infection risks between 4% and 11%, the preferred option is to evacuate for a short period, vaccinate, and then reoccupy once the vaccine has taken effect. For risks between 0.003% and 4%, the preferred option is to vaccinate only. For risks below 0.003%, none of the mitigation actions have positive expected monetary benefits. A sensitivity analysis indicates that for high‐infection‐likelihood scenarios, vaccination is recommended in the case where decontamination efficacy is less than 99.99%.     

Foot-and-Mouth Disease Entrance Assessment Model Through Air Passenger Violations

This article aims to construct a risk model for the prediction of foot-and-mouth disease (FMD) entrance caused by passengers who illegally carry meat products of cloven-hoofed animals through international airports into a country. The risk that meat contaminated with the FMD virus is formulated as the probabilities of FMD factor events (the prevalence of FMD), the commodity factor event (the transportation, storage, and distribution (TSD) factor event), and the passenger event. Data used for analysis were records of illegal meat product carriers from areas A and B intercepted at an international airport in Taiwan. A risk model was proposed to simulate the probability distributions in disease prevalence, probability of FMD virus existing in the meat products after meat processing, and estimation of survival of virus and time period for TSD. The probability of the passenger event was hypothesized with the odds of intercepted passengers and estimated via logistic regression. The results showed that the odds of passengers being intercepted by beagles were higher than those intercepted by Customs. By conducting Monte Carlo simulations, the probability of FMD virus risk caused by FMD factors from area A was 149 times lower than that from area B. The probability of FMD virus risk caused by the passenger event from area A was four times lower than the corresponding probability from area B. The model provides a contribution to FMD prevention and can be a reference for developing models of other diseases.     

Passenger and pilot risk minimization in offshore helicopter transportation

In the offshore petroleum industry, employees are transported to and from the offshore installations by helicopter, which represents a major risk. This paper analyzes how to improve transportation safety by solving the helicopter routing problem with a risk objective expressed in terms of expected number of fatalities. A mathematical model is proposed and a tabu search heuristic is applied to this problem. Three routing policies are considered: a direct routing policy, a Hamiltonian routing policy, and a general routing policy. Extensive computational experiments are conducted on instances derived from real data in order to assess and compare these policies under a travel time, a passenger risk and a combined passenger and pilot risk objective. Several management insights can be derived from this study. In particular, our results show that passenger transportation risk can be reduced by increasing travel time at the expense of pilot risk. This can be achieved through a reduction of the average number of passengers onboard by applying either a Hamiltonian or a general routing policy. Our methodology can also be used to derive an equitable distribution of risk between passengers and pilots, considering that pilots fly much more frequently than passengers.     

Development and application of a dose–response model for Elizabethkingia spp

Elizabethkingia spp. are common environmental pathogens responsible for infections in more vulnerable populations. Although the exposure routes of concern are not well understood, some hospital-associated outbreaks have indicated possible waterborne transmission. In order to facilitate quantitative microbial risk assessment (QMRA) for Elizabethkingia spp., this study fit dose–response models to frog and mice datasets that evaluated intramuscular and intraperitoneal exposure to Elizabethkingia spp. The frog datasets could be pooled, and the exact beta-Poisson model was the best fitting model with optimized parameters α  = 0.52 and β = 86,351. Using the exact beta-Poisson model, the dose of Elizabethkingia miricola resulting in a 50% morbidity response (LD₅₀) was estimated to be approximately 237,000 CFU. The model developed herein was used to estimate the probability of infection for a hospital patient under a modeled exposure scenario involving a contaminated medical device and reported Elizabethkingia spp. concentrations isolated from hospital sinks after an outbreak. The median exposure dose was approximately 3 CFU/insertion event, and the corresponding median risk of infection was 3.4E-05. The median risk estimated in this case study was lower than the 3% attack rate observed in a previous outbreak, however, there are noted gaps pertaining to the possible concentrations of Elizabethkingia spp. in tap water and the most likely exposure routes. This is the first dose–response model developed for Elizabethkingia spp. thus enabling future risk assessments to help determine levels of risk and potential effective risk management strategies.     

A QMRA for the Transmission of ESBL‐Producing Escherichia coli and Campylobacter from Poultry Farms to Humans Through Flies

The public health significance of transmission of ESBL‐producing Escherichia coli and Campylobacter from poultry farms to humans through flies was investigated using a worst‐case risk model. Human exposure was modeled by the fraction of contaminated flies, the number of specific bacteria per fly, the number of flies leaving the poultry farm, and the number of positive poultry houses in the Netherlands. Simplified risk calculations for transmission through consumption of chicken fillet were used for comparison, in terms of the number of human exposures, the total human exposure, and, for Campylobacter only, the number of human cases of illness. Comparing estimates of the worst‐case risk of transmission through flies with estimates of the real risk of chicken fillet consumption, the number of human exposures to ESBL‐producing E. coli was higher for chicken fillet as compared with flies, but the total level of exposure was higher for flies. For Campylobacter, risk values were nearly consistently higher for transmission through flies than for chicken fillet consumption. This indicates that the public health risk of transmission of both ESBL‐producing E. coli and Campylobacter to humans through flies might be of importance. It justifies further modeling of transmission through flies for which additional data (fly emigration, human exposure) are required. Similar analyses of other environmental transmission routes from poultry farms are suggested to precede further investigations into flies.     

Validation and Application of Models to Predict Facemask Influenza Contamination in Healthcare Settings

Facemasks are part of the hierarchy of interventions used to reduce the transmission of respiratory pathogens by providing a barrier. Two types of facemasks used by healthcare workers are N95 filtering facepiece respirators (FFRs) and surgical masks (SMs). These can become contaminated with respiratory pathogens during use, thus serving as potential sources for transmission. However, because of the lack of field studies, the hazard associated with pathogen‐exposed facemasks is unknown. A mathematical model was used to calculate the potential influenza contamination of facemasks from aerosol sources in various exposure scenarios. The aerosol model was validated with data from previous laboratory studies using facemasks mounted on headforms in a simulated healthcare room. The model was then used to estimate facemask contamination levels in three scenarios generated with input parameters from the literature. A second model estimated facemask contamination from a cough. It was determined that contamination levels from a single cough (≈19 viruses) were much less than likely levels from aerosols (4,473 viruses on FFRs and 3,476 viruses on SMs). For aerosol contamination, a range of input values from the literature resulted in wide variation in estimated facemask contamination levels (13–202,549 viruses), depending on the values selected. Overall, these models and estimates for facemask contamination levels can be used to inform infection control practice and research related to the development of better facemasks, to characterize airborne contamination levels, and to assist in assessment of risk from reaerosolization and fomite transfer because of handling and reuse of contaminated facemasks.     

Analysis of Regional Scale Risk of Whirling Disease in Populations of Colorado and Rio Grande Cutthroat Trout Using a Bayesian Belief Network Model

Introduction and spread of the parasite Myxobolus cerebralis, the causative agent of whirling disease, has contributed to the collapse of wild trout populations throughout the intermountain west. Of concern is the risk the disease may have on conservation and recovery of native cutthroat trout. We employed a Bayesian belief network to assess probability of whirling disease in Colorado River and Rio Grande cutthroat trout (Oncorhynchus clarkii pleuriticus and Oncorhynchus clarkii virginalis, respectively) within their current ranges in the southwest United States. Available habitat (as defined by gradient and elevation) for intermediate oligochaete worm host, Tubifex tubifex, exerted the greatest influence on the likelihood of infection, yet prevalence of stream barriers also affected the risk outcome. Management areas that had the highest likelihood of infected Colorado River cutthroat trout were in the eastern portion of their range, although the probability of infection was highest for populations in the southern, San Juan subbasin. Rio Grande cutthroat trout had a relatively low likelihood of infection, with populations in the southernmost Pecos management area predicted to be at greatest risk. The Bayesian risk assessment model predicted the likelihood of whirling disease infection from its principal transmission vector, fish movement, and suggested that barriers may be effective in reducing risk of exposure to native trout populations. Data gaps, especially with regard to location of spawning, highlighted the importance in developing monitoring plans that support future risk assessments and adaptive management for subspecies of cutthroat trout.     

Impact of Acquired Immunity and Dose‐Dependent Probability of Illness on Quantitative Microbial Risk Assessment

Dose‐response models in microbial risk assessment consider two steps in the process ultimately leading to illness: from exposure to (asymptomatic) infection, and from infection to (symptomatic) illness. Most data and theoretical approaches are available for the exposure‐infection step; the infection‐illness step has received less attention. Furthermore, current microbial risk assessment models do not account for acquired immunity. These limitations may lead to biased risk estimates. We consider effects of both dose dependency of the conditional probability of illness given infection, and acquired immunity to risk estimates, and demonstrate their effects in a case study on exposure to Campylobacter jejuni. To account for acquired immunity in risk estimates, an inflation factor is proposed. The inflation factor depends on the relative rates of loss of protection over exposure. The conditional probability of illness given infection is based on a previously published model, accounting for the within‐host dynamics of illness. We find that at low (average) doses, the infection‐illness model has the greatest impact on risk estimates, whereas at higher (average) doses and/or increased exposure frequencies, the acquired immunity model has the greatest impact. The proposed models are strongly nonlinear, and reducing exposure is not expected to lead to a proportional decrease in risk and, under certain conditions, may even lead to an increase in risk. The impact of different dose‐response models on risk estimates is particularly pronounced when introducing heterogeneity in the population exposure distribution.