title: Temporal percolation of the susceptible network in an epidemic spreading.
abstract: 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. As a consequence, in order to preserve a macroscopic connected fraction of the network composed by healthy individuals which guarantee its functionality, any mitigation strategy should be implemented before this critical time t(c). Our theoretical results are confirmed by extensive simulations of the SIR process.
authors.affiliation: Facultad de Ciencias Exactas y Naturales, Instituto de Investigaciones Físicas de Mar del Plata-Departamento de Física, Universidad Nacional de Mar del Plata, Mar del Plata, Argentina. ldvaldes@mdp.edu.ar
authors.forename: Lucas Daniel
authors.initials: LD
authors.lastname: Valdez
authors.forename: Pablo Alejandro
authors.initials: PA
authors.lastname: Macri
authors.forename: Lidia Adriana
authors.initials: LA
authors.lastname: Braunstein
mesh_terms: D000465:Algorithms; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D004198:Disease Susceptibility / Q000453:epidemiology*; D058872:Epidemics; D006801:Humans; D008962:Models, Theoretical