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Fast and exact stochastic simulations of epidemics on static and temporal networks

Fig 2

Epidemics on temporal networks.

Illustration of the temporal simulation algorithm. A link from node i to node j appears and disappears after node i has been infected at time T_i. Upon appearing at time t₁, the link is “activated”, i.e., a time between infection and transmission is drawn from . Here, the condition ensures that the time lies in the future, i.e. after t₁. However, before the simulation reaches time , the link disappears, , causing the algorithm to mask the link. Since the link is still masked when transmission is attempted at time , the attempt is blocked. The link is then unmasked so that when it reappears at time t₂, it is re-activated, i.e. a time until transmission (again conditioned to lie in the future, i.e. after t₂) is drawn. Further disappearances and reappearances of the link before time then do not cause further activations but merely change the state of the link. Once the simulation reaches time , the disease is then transmitted to node j since the link happens to be unmasked at that time. See S1 Algorithms for a detailed description of the algorithm.

doi: https://doi.org/10.1371/journal.pcbi.1013490.g002