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arXiv · 1206.2720

Temporal percolation of the susceptible network in an epidemic spreading

L. D. Valdez·P. A. Macri·L. A. Braunstein
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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 $Φ_S(t)$, 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.

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L. D. Valdez, P. A. Macri, L. A. Braunstein. 2012-09-23. Temporal percolation of the susceptible network in an epidemic spreading. https://doi.org/10.1371/journal.pone.0044188

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