Inferring country-specific import risk of diseases from the world air transportation network
Fig 2
Starting from the transition network (left) the shortest path tree is computed based on the effective distance (center bottom). Based on the shortest path tree, the exit probabilities q∘ = q(∘|⋆) are computed. In the formula, the geometric symbols represent the estimated population of the respective node, which can also be distance-weighted (depending on the exact model). A random walk-process with exit probability is defined (top): at each step, the walker either exits the node with prob. q∘ = q(∘|⋆), or continues walking with prob. (1 − q∘). The import risk p∞(∘|⋆) (right) is the probability of a walker to exit at node ∘ given it started at node ⋆ under consideration of all possible paths.