Inferring country-specific import risk of diseases from the world air transportation network

Disease propagation between countries strongly depends on their effective distance, a measure derived from the world air transportation network (WAN). It reduces the complex spreading patterns of a pandemic to a wave-like propagation from the outbreak country, establishing a linear relationship to the arrival time of the unmitigated spread of a disease. However, in the early stages of an outbreak, what concerns decision-makers in countries is understanding the relative risk of active cases arriving in their country—essentially, the likelihood that an active case boarding an airplane at the outbreak location will reach them. While there are data-fitted models available to estimate these risks, accurate mechanistic, parameter-free models are still lacking. Therefore, we introduce the ‘import risk’ model in this study, which defines import probabilities using the effective-distance framework. The model assumes that airline passengers are distributed along the shortest path tree that starts at the outbreak’s origin. In combination with a random walk, we account for all possible paths, thus inferring predominant connecting flights. Our model outperforms other mobility models, such as the radiation and gravity model with varying distance types, and it improves further if additional geographic information is included. The import risk model’s precision increases for countries with stronger connections within the WAN, and it reveals a geographic distance dependence that implies a pull- rather than a push-dynamic in the distribution process.Author summary: For the spread of a contagious disease, human mobility puts distant places in proximity and geographically closer targets may be effectively much further away. The worldwide flight network is crucial for long distance travels and the previously proposed ‘effective distance’ translates this mobility into a distance measure that correlates with the disease arrival time. We use the effective distance to generate a bottom-up and thus parameter-free distribution process of passengers on the flight network, which takes into account all possible flight routes. This allows us to determine the import probability of a disease. Our ‘import risk’ model outperforms or matches established mobility models, some of which require calibration with scarce or costly data. In contrast, our approach relies on minimal flight network data, that is the number of planes between airports and their passenger capacities, but not on passenger data. Its bottom-up approach enables future studies on country-specific measures for controlling and containing infected passengers, a challenge with existing models. Thus, the ‘import risk’ model’s strength lies in its data simplicity, this relevance to pandemics, and parameter-free design.