Outbreaks in susceptible-infected-removed epidemics with multiple seeds

TL;DR

This paper analyzes the phase transitions in a susceptible-infected-removed epidemic model with multiple initial infection seeds on a network, revealing that epidemic clusters percolate before a global outbreak occurs as infection rate increases.

Contribution

It derives percolation transition points for the SIR model with multiple seeds, highlighting differences from single-seed epidemic thresholds.

Findings

Epidemic clusters percolate prior to a global outbreak.

Two distinct percolation transitions are identified.

Finite seed fractions significantly affect epidemic phase transitions.

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.