Abstract
Epidemic models are used across biological and social sciences, engineering, and computer science, and have had important impact in the study of the dynamics of human disease and computer viruses, but also trends rumors, viral videos, and most recently the spread of fake news on social networks. In this paper, we focus on epidemics propagating on a graph, as introduced by the seminal paper [5]. In particular, we consider so-called SI models (see below for a precise definition) where an infected node can only propagate the infection to its non-infected neighbor, as opposed to the fully mixed models considered in the early literature. This graph-based approach provides a more realistic model, in which the spread of the epidemic is determined by the connectivity of the graph, and accordingly some nodes may play a larger role than others in the spread of the infection.
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