Dynamic percolation of the susceptible network in a epidemic spreading

LUCAS D. VALDEZ; P. A. MACRI; L. A. BRAUNSTEIN

PLOS ONE

PUBLIC LIBRARY SCIENCE

Lugar: San Francisco; Año: 2012

1932-6203

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 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.