Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of initial infection size on network SIR model   We consider the effect of a nonvanishing fraction of initially infected nodes
(seeds) on the SIR epidemic model on random networks. This is relevant when,
for example, the number of arriving infected individuals is large, but also to
the modeling of a large number of infected individuals, but also to more
general situations such as the spread of ideas in the presence of publicity
campaigns. This model is frequently studied by mapping to a bond percolation
problem, in which edges in the network are occupied with the probability, $p$,
of eventual infection along an edge connecting an infected individual to a
susceptible neighbor. This approach allows one to calculate the total final
size of the infection and epidemic threshold in the limit of a vanishingly
small seed fraction. We show, however, that when the initial infection occupies
a nonvanishing fraction $f$ of the network, this method yields ambiguous
results, as the correspondence between edge occupation and contagion
transmission no longer holds. We propose instead to measure the giant component
of recovered individuals within the original contact network. This has an
unambiguous interpretation and correctly captures the dependence of the
epidemic size on $f$. We give exact equations for the size of the epidemic and
the epidemic threshold in the infinite size limit. We observe a second order
phase transition as in the original formulation, however with an epidemic
threshold which decreases with increasing $f$. When the seed fraction $f$ tends
to zero we recover the standard results.

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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph