Outbreaks in susceptible-infected-removed epidemics with multiple seeds

Abstract

We study a susceptible-infected-removed (SIR) model with multiple seeds on a regular random graph. Many researchers have studied the epidemic threshold of epidemic models above which a global outbreak can occur, starting from an infinitesimal fraction of seeds. However, there have been few studies of epidemic models with finite fractions of seeds. The aim of this paper is to clarify what happens in phase transitions in such cases. The SIR model in networks exhibits two percolation transitions. We derive the percolation transition points for the SIR model with multiple seeds to show that as the infection rate increases epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak.

14 pages, 9 figures

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• Criticality in spreading processes without time-scale separation and the critical brain hypothesis
• Epidemic control in networks with cliques
• Critical behavior of a two-step contagion model with multiple seeds
• Sudden spreading of infections in an epidemic model with a finite seed fraction
• Synergistic epidemic spreading in correlated networks
• Modeling and Controlling the Spread of Epidemic with Various Social and Economic Scenarios
• Identifying influential subpopulations in metapopulation epidemic models using message-passing theory