Scaling Expected Force: Efficient Identification of Key Nodes in Network-Based Epidemic Models

Structural centrality measures are often used to approximate or predict dynamical influence in a network. The recently proposed Expected Force of Infection (ExF) measures the entropy of all potential transmission paths starting at a node, effectively characterizing a node's role in epidemic diffusion processes. However, this promising metric has seen limited adoption mainly due to an inefficient formulation and the lack of an open-source implementation. In this paper, we present a novel cluster-centric, parallel algorithm enhancing ExF's efficiency and scalability. Compared to the simple parallel version of the original formulation of the ExF our efficient, open-source GPU implementation enables key nodes detection at previously intractable scales, with speed-ups of up to 300 x on networks with up to 44 million edges. Leveraging on our algorithm, we compare the ExF with other well-known centrality metrics, upon six real and synthetic contact networks. The ExF emerges as the best of the considered metrics in a few, important tasks: it predicts the likelihood of a global epidemic and its diffusion speed, based on the centrality of the seed node; and it predicts how many other infections will occur as a consequence, in some sense, of a specific node having caught the disease.