Predicting the Speed of Epidemics Spreading in Networks.

Global transport and communication networks enable information, ideas, and infectious diseases to now spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like processes, there is a need to predict the speed of a particular contagion in a particular network, and to distinguish between nodes that are more likely to become infected sooner or later during an outbreak. Here, we study these quantities using a message-passing approach to derive simple and effective predictions that are validated against epidemic simulations on a variety of real-world networks with good agreement. In addition to individualized predictions for different nodes, we find an overall sudden transition from low density to almost full network saturation as the contagion progresses in time. Our theory is developed and explained in the setting of simple contagions on treelike networks, but we are also able to show how the method extends remarkably well to complex contagions and highly clustered networks.