Temporal percolation of the susceptible network in an epidemic spreading

TL;DR

This paper analyzes how the susceptible network in an epidemic evolves over time using percolation theory, identifying a critical point where the network's giant component disintegrates, informing optimal intervention timing.

Contribution

It introduces a time-dependent percolation framework for the susceptible network in SIR epidemics, revealing a critical time for network disintegration and implications for mitigation strategies.

Findings

Existence of a critical time $t_c$ for network disintegration

The susceptible network's giant component is destroyed after $t_c$

Mitigation should be implemented before $t_c$

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 $\Phi_S(t)$, 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.