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Outbreaks in susceptible-infected-removed epidemics with multiple seeds

Takehisa Hasegawa and Koji Nemoto
Phys. Rev. E 93, 032324 – Published 30 March 2016

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.

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  • Received 29 October 2015
  • Revised 5 March 2016

DOI:https://doi.org/10.1103/PhysRevE.93.032324

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Networks

Authors & Affiliations

Takehisa Hasegawa1,* and Koji Nemoto2,†

  • 1Department of Mathematics and Informatics, Ibaraki University, 2-1-1 Bunkyo, Mito 310-8512, Japan
  • 2Department of Physics, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810, Japan

  • *takehisa.hasegawa.sci@vc.ibaraki.ac.jp
  • nemoto@statphys.sci.hokudai.ac.jp

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Issue

Vol. 93, Iss. 3 — March 2016

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