The Nodes:
Nodes in the network represent the largest 1227 airports in the worldwide air-transportation network (WAN) comprising approx. 95% of the entire global air traffic. The dataset used in our computational models contains more than 4000 airports, a total passenger flux of more than 3 billion passengers/year. Node size quantifies the capacity (size) of an airport. Colors correspond to geographical regions. Hover over a node for an additional info pop-up.
(close window)
The Tree:
The tree represents the collection of most probable spreading pathways of a disease that enters at the root node. Given the outbreak origin (the root node, bottom of the tree). The vertical distance in the tree is the effective distance from the outbreak origin. The concept of effective distance was introduced in our recent paper The hidden geometry of complex, network-driven contagion phenomena, Science (2013). Effective distance is a much better predictor of arrival times and import probabilities than geographical distance. Although the method cannot predict what the absolute arrival time at a given node is, we can nevertheless predict the expected sequence or airports in the arrival chain. Depending on the chosen root node (outbreak origin) airports can play different roles in terms of further distributing of a disease. They can have different distribution propensities: the number of off-branches or “children” in the tree.
(close window)
Relative Import Probability:
The probability that an infected individual arrives at any location in the worldwide air-transportation network (S) is the product of 2 quantities: 1.) The probability that a patient boards a plane at an outbreak location (Q) multiplied by the probability that the patient takes one among very many possible routes to a destination and gets off the plane (P):
S = Q x P
If, for example, the first probability is Q=1/10000 and the second probability is P=1/10, the total probability is S=1/100000. The first component of the probability is difficult to estimate, the second part can be computed using a computational model for movement patterns on the worldwide air-transportation network. This second quantity (P) is called the relative import risk: Given that an infected individual boards a plane at airport X, what is the probability that the person arrives at point Y.
It is important to understand that the absolute (actual) import risk is much much lower than the relative import risk. The relative risk is only useful for comparing different locations and alone does not predict the import probability at a certain destination.
(close window)
Effective Distance:
When viewing the time course of the spread of an infectious disease on a global scale on a conventional geographic map, the patterns are complex. This complexity is a consequence of the complicated way locations are connected by the worldwide air-transportation network. Geographic distance is not a good predictor for how long it will take for an "epidemic wave" with a certain outbreak location to reach a different part of the world. Effective distance is a novel type of distance measure which is computed from the traffic flux along links on the air-transportation network. In a nutshell, places that exchange lots of passengers are closer than places that exchange a few. The underlying mathematics is a bit more involved than this, however. When remapping the world using effective distance and looking at it from the perspective of the outbreak location, spreading phenomena possess a simple wave-like propagation geometry, see for example this animation of a computer simulated pandemic. Because of the simplicity of the pattern, we can use effective distance to predict relative arrival times.
(close window)
The Computational Model:
The Relative Import Risk (ReIP) at every node is computed with a stochastic, dynamical model that simulates travel movement patterns on the worldwide airtransportation network. The foundation of the model is data on passenger flux between 4069 airports that are connected by approx. 25000 links. From this data we compute the probabilities that an individual at an airport travels to another connected airport. Arriving at an airport we estimated the probability that a passenger continues a journey or stays at the location. This dynamic model is combined with a recent model that accounts for the most probable paths that connect an arbitrary pair of nodes in the network. A manuscript with a detailed account of the model an various applications is in preparation.
(close window)
Origin Selection:
The list of choices in the top left contain two different types of origins. Two locations are chosen from countries that have case reports or unconfirmed cases (red). To each of these there are comparison cases where a single, important airline connection has been cut (knock-outs, green). These are illustrative examples for understanding how airline traffic modifications chance the structure of the most probable spreading pathways and associated import probabilities.
(close window)