Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical scaling of stochastic epidemic models   In the simple mean-field SIS and SIR epidemic models, infection is
transmitted from infectious to susceptible members of a finite population by
independent $p-$coin tosses. Spatial variants of these models are proposed, in
which finite populations of size $N$ are situated at the sites of a lattice and
infectious contacts are limited to individuals at neighboring sites. Scaling
laws for both the mean-field and spatial models are given when the infection
parameter $p$ is such that the epidemics are critical. It is shown that in all
cases there is a critical threshold for the numbers initially infected: below
the threshold, the epidemic evolves in essentially the same manner as its
branching envelope, but at the threshold evolves like a branching process with
a size-dependent drift.

33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th