Air travel is an increasingly important conduit for the worldwide spread of infectious diseases, enabling pathogens to spread across vast distances, transported by infected travellers. Outbreaks of infectious diseases can have severe impacts on human health, animal health, and the economy (Golnar et al., 2016). The rapid, global spread of COVID-19 from Wuhan, China (Bogoch et al., 2020) clearly demonstrates the dramatic influence our global transportation networks have on the domestic and international spread of disease. Similarly, the spread of SARS into 29 countries within a six-month period, the importation of Ebola virus into the United States, the spread of Zika virus into and across the Americas, and the importation of Yellow Fever to multiple countries in Africa, Asia, Europe, and South America were largely driven by domestic and international air travel (Bilotkach et al., 2012; Brent et al., 2018; Cliff and Haggett, 2004; European Centre for Disease Prevention and Control, 2018; Golnar et al., 2016; Hatcher et al., 2012; Kilpatrick et al., 2006; Powers, 2015; WHO, 2020). In effect, evaluating the potential for local infectious disease spread in a destination connected to an outbreak for global infectious disease prediction could substantially improve subnational accuracy and precision for early warning systems and scenario planning. However, rarely are data available regarding which origin airports infected travellers might use to initiate travel, and where travellers might go to after reaching their final airport destination (Bogoch et al., 2015; Bogoch et al., 2016a,b; Tatem et al., 2012; Tuite et al., 2019). This knowledge gap can be addressed by modelling airport catchment areas.

Airport catchment areas are defined as the geographic extent that captures the area in which an airport derives most of its patronage (Hernandez et al., 2004). Within an airport’s catchment area, probability to use the airport may vary spatially (Fuellhart, 2007). Airport catchment areas are commonly estimated using deterministic methods, such as circular buffers or Thiessen polygons (Arino and Khan, 2015; Brent et al., 2018; Semenza et al., 2014). These approaches grossly over-simplify the representation of catchment areas. Circular buffers assume that individuals travel a defined distance, such as 200 km, to or from airports (Bilotkach et al., 2012; McLay and Reynolds-Feighan, 2006; Wang, 2000; Wittman, 2014). The circular buffers approach often only includes proximity to or from an airport, and does not consider the attractiveness of each airport. Service frequency, quality of service, and airfares are examples of factors that affect a traveller’s choice, and contribute to overall airport attractiveness (Leon, 2011; Lin et al., 2016). The Thiessen polygons approach assumes that individuals will always travel the shortest possible distance to reach an airport (Hernandez et al., 2004). While this approach can incorporate a representation of airport attractiveness using weighted Thiessen polygons (Boots, 1980), it does not account for overlap among multiple airport catchment areas.

Accounting for overlap among multiple airport catchment areas is particularly relevant in cases where multiple airports are located within close proximity and serve common populations (Fuellhart, 2007; Kim and Ryerson, 2018; Lieshout, 2012; Paliska et al., 2016). For example, John F. Kennedy International, La-Guardia, and Newark Liberty International are major airports in the U.S. states of New York and New Jersey that are less than 45 km from each other, and Dulles International, Baltimore-Washington International, and Ronald Reagan Washington International are major airports in the states of Virginia, Maryland, and District of Colombia less than 95 km from each other. There is likely overlap between the catchment areas for airports within these clusters. Furthermore, both deterministic methods assume there is no variation in the likelihood to use an airport within the catchment area (Hernandez et al., 2004; Wittman, 2014).

By comparison, probabilistic approaches do not assume that individuals choose an airport solely based on proximity, but estimate the likelihood that a population would use one or more airports for travel (Hernandez et al., 2004; Lin et al., 2016). Therefore, using a probabilistic approach may improve the accuracy in approximating the airports an individual departing an outbreak-affected country is likely to use, or conversely the regions in destinations potentially receiving passengers arriving from outbreak-affected countries. More complex probabilistic methods have been applied to define catchment areas for a single airport or airport region (Lieshout, 2012), but these methods require numerous input parameters that make it impractical to estimate catchment areas for large geographic areas with a large number of airports. In contrast, the Huff model is a simple, but probabilistic method that offers an alternative to deterministic approaches and requires only a few input parameters. Based on the Huff model, the probability that someone would use an airport is defined largely by two main factors: 1) distance to each surrounding airport, and 2) a measure of attractiveness for each surrounding airport, such as flight or traveller volume (Huff, 2003). While the Huff model was originally developed to predict consumer patronage patterns for retail (Huff, 1963), and has been applied to transportation scenarios (Lin et al., 2016), to our knowledge there is limited literature on its application in defining airport catchment areas for public health.

Given the lack of established catchment areas for most airports within the United States and internationally, a dearth in openly-accessible individual-level mobility data (Golnar et al., 2016), and few corresponding modelling techniques, we examine a proof of concept for the Huff model as a potential decision-support tool to help estimate spread of dangerous infectious diseases at a local level. We qualitatively explored the sensitivity of the Huff model to varying input parameters on estimated airport catchment areas: distance decay exponent, distance cut-off, and measures of airport attractiveness. We examined the potential application of the Huff model using two case studies: Miami International Airport (MIA) and Harrisburg International Airport (MDT), respectively. We specifically compared our model output to observed data sampled for MDT from a previous study to align model parameters with an established, observed catchment area.

We applied the Huff model to estimate the probability that residents living in each census tract within the United States would use any airport within the United States, when departing for an international destination. Results were calculated at the census tract level, a commonly used spatial boundary for public health policy decisions (Krieger, 2006). This probability of individuals at census tract i to choose airport j is described by (Huff, 2003): Pij=Sj  a/Dij  β∑i=1nSj  a/Dij  β where Sj is a measure of attractiveness for airport j, Dij is the distance from census tract i to airport j, α is an airport attractiveness exponent, and β is the distance decay exponent.

Distance between each census tract i and each airport j was measured using Euclidean (straight line) distance. To optimize the algorithm, we applied a distance cut-off to define a subset of airports (referred to as the choice set) considered to be viable alternatives for each census tract. The distance cut-off should reflect the maximum distance an individual would plausibly travel to reach an airport (Huff and Black, 1997). The Huff model uses a distance decay exponent β to represent the impact of distance on the choice of airport; a smaller exponent means that distance has a lower impact on individuals’ choice of airport and is usually used for goods or services that are not widely available, where the opposite is true for a larger exponent (Esri, 2016; Huff, 1963). The exponent typically ranges between 1 and 3 in the Huff model literature (Esri, 2016; Hernandez et al., 2004). The attractiveness variable S is a measure of attractiveness of each airport j to the potential traveller. We assumed that the total volume of outbound international travellers at each airport was a reasonable proxy for airport attractiveness (see supplementary materials). The attractiveness exponent α represents how attractiveness affects the individual’s choice of airport; a smaller exponent means that attractiveness has a weaker draw on a individual’s selection of airport, where the opposite is true for a larger exponent.

While the Huff model most directly estimates probability to use an airport from a given census tract based on outbound travel, we assume symmetric airport use whereby travellers who use a specific airport to travel outbound will use the same airport to return home after arrival in their home country.

To assess the risks of infectious disease spread in today’s highly interconnected world, public health officials must consider how ground travel and air travel intersect. In the event of a global pandemic, air travel data has been shown to be predictive of destination cities or regions most at risk of imported cases of infectious diseases. However, the area in which arriving passengers locally disperse after arrival at a destination airport is often unknown. Our methods explore how the Huff model might more accurately identify which airports an individual departing an outbreak area may use, as well as delineate local areas more at risk of receiving imported cases after individuals arrive at an airport from an outbreak-affected country. Indeed, adapting geospatial methods that generalize the catchment areas for any given airport could improve the geographic accuracy by which containment measures or targeted communication campaigns are executed. Furthermore, results could be leveraged to improve the precision of early warning systems that anticipate infectious disease spread. Our study specifically examined the Huff model, which we used to estimate catchment areas for two commercial airports in the United States. We analyzed results for Miami International Airport (MIA) because of its presumed role as the introduction source for Zika virus to the Miami area in 2016. We also studied Harrisburg International Airport (MDT), and compared our findings with those from an earlier study (Fuellhart, 2007).

Our evaluation of model sensitivity to changes in inputs parameters demonstrated that parameter choice should be considered carefully, specifically for the distance decay exponent and the distance cut-off. First, based on our case studies, applying a distance decay exponent of 2 resulted in a more reasonable representation of the effect of distance on individuals’ willingness to travel to an airport as compared to the other selected inputs. For the MIA test case, exponents of 1.5 and 2 resulted in the expected decrease in probability to travel from census tracts with increasing distance from MIA, or with increasing proximity to other major airports. Furthermore, results with a distance decay exponent of 2 had the highest level of agreement with the sample of observed MDT users.

Second, the distance cut-off of 500 km appeared most reasonable based on the relative findings from our MIA and MDT scenarios. In the MIA sensitivity analysis, the 500 km cut-off did not extend outside of Florida, but also did not restrict the catchment area to only a small area of southern Florida (both of which seemed unrealistic). When paired with the distance decay exponent of 2, the 500 km cut-off allowed for a gradual decrease in probability over distance; 200 km resulted in a drastic decrease from greater than 40% to 0% at the cut-off, while 1000 km resulted in an increase in probability after approximately 650 km (when considering the travel destination of Brazil). Moreover, when a 500 km cut-off was applied in the MDT scenario, model outputs were very similar to the observed data.

Third, we found that using travel volume to the specific international destination of Brazil (versus all international travel) had little impact on the predicted choice of airport when the highlighted distance decay exponent and distance cut-off (2 and 500 km, respectively) were applied. However, we expect that the choice of airport might be different for domestic versus international travel; there would be dramatic differences in probability in cases where airports had only domestic flights.

There are notable differences between our estimated catchment areas produced by the Huff model and those produced by other methods that have been applied in existing literature (i.e. circular buffers and using Primary Statistical Areas as a proxy). In comparison to a 200 km buffer, some similarities exist. For example, in most outputs the area our model estimated to have greater than 40% probability to use MIA was similar in extent to a 200 km buffer. However, our model’s results may be more realistic than the 200 km buffer because they reflect lower probability to use MIA for census tracts close to other attractive airports, such as Fort Lauderdale International Airport (FLL) located north of MIA, which aligns with findings from multiple studies that suggest that distance/access time has a notable impact on airport choice (Başar and Bhat, 2004; Hess and Polak, 2005; Ishii et al., 2009; Leon, 2011; Lieshout, 2012; Pels et al., 2003; Suzuki, 2007). Moreover, a 200 km buffer would likely over-estimate the catchment area for smaller, less attractive airports. In contrast, it would likely under-estimate the catchment area for highly attractive airports, especially for those that have few other attractive airport options nearby.

Additionally, for our test cases the Huff model predicted larger airport catchment areas than would be predicted by using Primary Statistical Area (PSA) boundaries (Supplementary Fig. 1). The United States Census Bureau divides the country into PSAs associated with a variety of census data tailored to each region (Wittman, 2014) (see supplementary materials). For example, the overall catchment area estimated by the Huff model for MDT is larger than the PSA boundary for this area, though most areas that the Huff model estimated to have a high proportion of MDT users would fall within it. Also, as a deterministic method the PSA boundary assumes that within its boundary there is no variation in probability for travellers to use MDT; our model accounts for such variation.

Our study has a number of limitations. First, we limited our evaluation of the Huff model to only two airports (MIA and MDT) within the United States. Other airports in the United States or internationally may differ in their catchment area parameters, depending on the number of feasible airport options, population characteristics, or varying access to transportation infrastructure. For example, access to a personal vehicle or to rail infrastructure would likely influence willingness to travel further distances to reach an airport. Second, the results of our model are more applicable to residents than to tourists. We assumed that residents will deplane and travel to their place of residence, but various factors will influence where a tourist will travel and disperse from a given airport. It is possible that a separate model is required to estimate catchment areas for tourists. Third, we used itinerary-level traveller volume as a proxy for all factors that represent the attractiveness of an airport but including multiple factors to represent attractiveness (such as airfares or flight frequency) might improve results. The trade-off between possible increases in model predictive power and model parsimony requires further evaluation. Fourth, we measured distance using Euclidean distance; road network distance or drive-time may be more accurate but requires greater computational resources, especially for a large study area such as the United States. Relative differences between Euclidean distance and road-network based measures would be most drastic where a physical barrier, such as a mountain or a water body, was present. Finally, calibration of parameter inputs and validation of results were restricted by the limited observed data. We did not have access to observed data for MIA to validate the estimated catchment area based on our selected inputs to the Huff model. Observed data for MDT was available from an existing study, so validation was conducted on results for this airport. Data for MDT was based on the parked cars of a sample of MDT users, which had its own limitations (see supplementary materials).

A more thorough validation of results requires more detailed traveller information or empirical human mobility data to understand ground travel to and from multiple airports. While survey data such as that collected by Fuellhart (2007) could be used for validation, conducting surveys for multiple airports would require considerable time, resources, and analysis. Newly emerging data sources such as call detail records (CDR) or online social network (OSN) data (collected when users use location-enabled smartphone applications) (Barbosa-filho et al., 2018) could help to understand population mobility at a local or regional scale. Human mobility data derived by anonymized mobile devices has recently become publicly available in some regions, through academic research agreements or through proprietary contracts, and could be leveraged to calibrate and validate the Huff model. Local human mobility data could also be used to directly define the catchment areas on an ongoing basis (e.g. accounting for seasonal variation, etc.), though this may be cost-, time-, and resource-prohibitive.

Defining airport catchment areas is important for assessing the possibility of local-level spread of infectious disease outbreaks because they could help approximate 1) airports where an infected individual is most likely to travel outbound from the epicenter of an outbreak, and 2) the geographic area where an infected traveller might go after deplaning at their destination. For example, the importation of cases of ZIKV, and subsequent locally-acquired transmission of ZIKV in Wynwood, Miami (Florida Health, 2017), represents a scenario in which Huff model-derived catchment area results could have been utilized as a decision-support tool to select census tracts more likely to receive travellers arriving from ZIKV-affected countries and territories, and help identify where strategic infrastructure could been placed.

In the absence of empirical local human mobility data and in data-limited public health scenarios, the Huff model could be used to readily estimate airport catchment areas at any level of geographic unit within a reasonable spatial scale. This helps to address the need for improved global pandemic modelling predictions. We support that the Huff model may be an acceptable alternative to commonly-applied deterministic methods such as circular buffers or Thiessen polygons because the outputs are probabilistic and provide more variability within an approximated catchment area. However, this method requires further validation using emerging sources of local population mobility data, and may not be transferrable across geographic areas where non-automobile forms of land travel predominate (e.g. areas where trains are frequently used for regional travel). While this methodology could be used to estimate airport catchment areas and such estimations could help to better anticipate the spread of infectious disease via air travel, there is more work to be done before public health officials would be able to reliably use such results to make policy-level decisions. Future studies might offer a comparison to ground truth using quantitative methods in which both model outputs as well as the outputs from other methodologies could be rigorously compared to ground truth, thereby showing that their outputs were closer to truth (“better”) than the other methods. While empirical data generated by mobile devices show significant promise for public health applications, their use is complicated by the size of the datasets, the skills required to manipulate and analyze these high spatiotemporal resolution data, questions about the representativeness of the data, and other challenges related to privacy and data security.