On the Treatment of Airline Travelers in Mathematical Models

Massey University, New Zealand
PLoS ONE (Impact Factor: 3.23). 07/2011; 6(7):e22151. DOI: 10.1371/journal.pone.0022151
Source: PubMed


The global spread of infectious diseases is facilitated by the ability of infected humans to travel thousands of miles in short time spans, rapidly transporting pathogens to distant locations. Mathematical models of the actual and potential spread of specific pathogens can assist public health planning in the case of such an event. Models should generally be parsimonious, but must consider all potentially important components of the system to the greatest extent possible. We demonstrate and discuss important assumptions relative to the parameterization and structural treatment of airline travel in mathematical models. Among other findings, we show that the most common structural treatment of travelers leads to underestimation of the speed of spread and that connecting travel is critical to a realistic spread pattern. Models involving travelers can be improved significantly by relatively simple structural changes but also may require further attention to details of parameterization.

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    • "However, the prediction seemed poor at the lower tail. This was expected, given likely randomness in the smaller amount of passenger exchanges between airports [17]. Diagnostic plots for other models are presented in figure S1 and S2. "
    [Show abstract] [Hide abstract] ABSTRACT: The expanding global air network provides rapid and wide-reaching connections accelerating both domestic and international travel. To understand human movement patterns on the network and their socioeconomic, environmental and epidemiological implications, information on passenger flow is required. However, comprehensive data on global passenger flow remain difficult and expensive to obtain, prompting researchers to rely on scheduled flight seat capacity data or simple models of flow. This study describes the construction of an open-access modeled passenger flow matrix for all airports with a host city-population of more than 100,000 and within two transfers of air travel from various publicly available air travel datasets. Data on network characteristics, city population, and local area GDP amongst others are utilized as covariates in a spatial interaction framework to predict the air transportation flows between airports. Training datasets based on information from various transportation organizations in the United States, Canada and the European Union were assembled. A log-linear model controlling the random effects on origin, destination and the airport hierarchy was then built to predict passenger flows on the network, and compared to the results produced using previously published models. Validation analyses showed that the model presented here produced improved predictive power and accuracy compared to previously published models, yielding the highest successful prediction rate at the global scale. Based on this model, passenger flows between 1,491 airports on 644,406 unique routes were estimated in the prediction dataset. The airport node characteristics and estimated passenger flows are freely available as part of the Vector-Borne Disease Airline Importation Risk (VBD-Air) project at:
    Full-text · Article · May 2013 · PLoS ONE
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    • "There has been considerable interest in the role of air travel, and possible air travel restrictions, on the spread of an infectious disease such as avian or 2009 A/H1N1 influenza, commonly called swine flu [7], [9], [10]. Previous studies have concluded that the net benefits to society of air travel restrictions are at best small [11]–[13], but most models rely on assumptions that have not been confronted with data [14]. What does seem clear is that flying increases the likelihood of air travelers contracting an infectious disease conditional on there being on infectious person on the airplane [15], [16], and that the public links flying with infection risk. "
    [Show abstract] [Hide abstract] ABSTRACT: Theory suggests that human behavior has implications for disease spread. We examine the hypothesis that individuals engage in voluntary defensive behavior during an epidemic. We estimate the number of passengers missing previously purchased flights as a function of concern for swine flu or A/H1N1 influenza using 1.7 million detailed flight records, Google Trends, and the World Health Organization's FluNet data. We estimate that concern over "swine flu," as measured by Google Trends, accounted for 0.34% of missed flights during the epidemic. The Google Trends data correlates strongly with media attention, but poorly (at times negatively) with reported cases in FluNet. Passengers show no response to reported cases. Passengers skipping their purchased trips forwent at least $50 M in travel related benefits. Responding to actual cases would have cut this estimate in half. Thus, people appear to respond to an epidemic by voluntarily engaging in self-protection behavior, but this behavior may not be responsive to objective measures of risk. Clearer risk communication could substantially reduce epidemic costs. People undertaking costly risk reduction behavior, for example, forgoing nonrefundable flights, suggests they may also make less costly behavior adjustments to avoid infection. Accounting for defensive behaviors may be important for forecasting epidemics, but linking behavior with epidemics likely requires consideration of risk communication.
    Full-text · Article · Mar 2013 · PLoS ONE
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    • "A range of uncertainties and limitations do still exist in the datasets and outputs presented however, and users are made aware of these within the full user guide and throughout the information boxes within the tool. Firstly, VBD-AIR considers only direct flights and their capacities within metric calculations, rather than actual passenger numbers or stopovers, and users are made aware of the uncertainties that this entails [43]. Within the disease and vector distribution modeling processes, uncertainties are inherent throughout [44], particularly in those regions with little field data to inform predictions. "
    [Show abstract] [Hide abstract] ABSTRACT: Background Over the past century, the size and complexity of the air travel network has increased dramatically. Nowadays, there are 29.6 million scheduled flights per year and around 2.7 billion passengers are transported annually. The rapid expansion of the network increasingly connects regions of endemic vector-borne disease with the rest of the world, resulting in challenges to health systems worldwide in terms of vector-borne pathogen importation and disease vector invasion events. Here we describe the development of a user-friendly Web-based GIS tool: the Vector-Borne Disease Airline Importation Risk Tool (VBD-AIR), to help better define the roles of airports and airlines in the transmission and spread of vector-borne diseases. Methods Spatial datasets on modeled global disease and vector distributions, as well as climatic and air network traffic data were assembled. These were combined to derive relative risk metrics via air travel for imported infections, imported vectors and onward transmission, and incorporated into a three-tier server architecture in a Model-View-Controller framework with distributed GIS components. A user-friendly web-portal was built that enables dynamic querying of the spatial databases to provide relevant information. Results The VBD-AIR tool constructed enables the user to explore the interrelationships among modeled global distributions of vector-borne infectious diseases (malaria. dengue, yellow fever and chikungunya) and international air service routes to quantify seasonally changing risks of vector and vector-borne disease importation and spread by air travel, forming an evidence base to help plan mitigation strategies. The VBD-AIR tool is available at Conclusions VBD-AIR supports a data flow that generates analytical results from disparate but complementary datasets into an organized cartographical presentation on a web map for the assessment of vector-borne disease movements on the air travel network. The framework built provides a flexible and robust informatics infrastructure by separating the modules of functionality through an ontological model for vector-borne disease. The VBD‒AIR tool is designed as an evidence base for visualizing the risks of vector-borne disease by air travel for a wide range of users, including planners and decisions makers based in state and local government, and in particular, those at international and domestic airports tasked with planning for health risks and allocating limited resources.
    Full-text · Article · Aug 2012 · International Journal of Health Geographics
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