id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
cord-010715-91fob3ax	Hasegawa, Takehisa	Outbreaks in susceptible-infected-removed epidemics with multiple seeds	2016-03-30		.txt	text/plain	5810	425	70	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. To evaluate the time evolution of the SIR dynamics and the total densities of the susceptible and removed nodes in the final states, we consider the approximate master equations (AMEs) [12, 14] . In particular, the gap between λ c1 and λ SIR c indicates that as the infection rate increases, the epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak. We have numerically and analytically shown that the present model with multiple seeds on the RRG percolates at a lower infection rate than the epidemic threshold. The SIR model with numerous seeds shows the percolation transition of the removed and susceptible nodes at λ c1 and λ c2 , respectively.	./cache/cord-010715-91fob3ax.txt	./txt/cord-010715-91fob3ax.txt