title: 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.
authors.affiliation: Department of Mathematics and Informatics, Ibaraki University, 2-1-1 Bunkyo, Mito 310-8512, Japan.
authors.forename: Takehisa
authors.initials: T
authors.lastname: Hasegawa
authors.affiliation: Department of Physics, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810, Japan.
authors.forename: Koji
authors.initials: K
authors.lastname: Nemoto
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D004198:Disease Susceptibility; D058872:Epidemics; D008962:Models, Theoretical