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Schematic representation of a compartmental contagion process on a network.

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posted on 2015-10-30, 03:54 authored by Christian L. Vestergaard, Mathieu Génois

(A) Illustration of a contagion process evolving on a time-varying network. Nodes’ colors correspond to their current state; edges denote current contacts between nodes; edge colors correspond to: black: no contagion may take place over the edge, red: contagion takes place during the present time-step, and red-to-blue gradient: contagion is possible but does not take place. (B) Example: reaction types in the SIR model. (C) Spontaneous reaction: a node i may spontaneously transition from its current state xi to xi with rate λm. (D) Contact-dependent reaction: a node i may transition from its current state xi to xi with rate λm upon contact with the node j in state xj. (E) Mixed transition: a node i may spontaneously transition from its current state xi to another state, xi with rate λm; contact with another node j, in state xj, may alter the transition rate of m, λmλm. After the contact (i, j)t ends, the transition rate may revert to λm, remain unchanged, or change to a third value.

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