Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks
Fig 1
Schematic representation of a compartmental contagion process on a network.
(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 with rate λm. (D) Contact-dependent reaction: a node i may transition from its current state xi to
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,
with rate λm; contact with another node j, in state xj, may alter the transition rate of m,
. After the contact (i, j)t ends, the transition rate may revert to λm, remain unchanged, or change to a third value.