Temporal percolation of the susceptible network in an epidemic spreading.

In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental approach and percolation tools, we find that a time-dependent quantity ΦS(t), namely, the probability that a given neighbor of a node is susceptible at time t, is the control parameter of a node void percolation process involving those nodes on the network not-reached by the disease. We show that there exists a critical time t(c) above which the giant susceptible component is destroyed.