L. D. Valdez, P. A. Macri, L. A. Braunstein
(Submitted on 13 Jun 2012)
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 top of complex networks. Using a edge-based compartmental approach and percolation tools, we find that the network composed by susceptible individuals undergoes a dynamic node percolation transition with a time dependent control parameter. We show that there exists a critical time $t_c$ above which the giant susceptible cluster is destroyed. As a consequence, in order to protect a large fraction of the susceptible individuals, any mitigation strategy should be implemented before this critical time $t_c$. Our theoretical results are confirmed by extensive simulations of the SIR process.