Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact deterministic representation of Markovian SIR epidemics on
  networks with and without loops   In a previous paper Sharkey et al. [13] proved the exactness of closures at
the level of triples for Markovian SIR (susceptible-infected-removed) dynamics
on tree-like networks. This resulted in a deterministic representation of the
epidemic dynamics on the network that can be numerically evaluated. In this
paper, we extend this modelling framework to certain classes of networks
exhibiting loops. We show that closures where the loops are kept intact are
exact, and lead to a simplified and numerically solvable system of ODEs
(ordinary-differential-equations). The findings of the paper lead us to a
generalisation of closures that are based on partitioning the network around
nodes that are cut-vertices (i.e. the removal of such a node leads to the
network breaking down into at least two disjointed components or subnetworks).
Exploiting this structural property of the network yields some natural
closures, where the evolution of a particular state can typically be exactly
given in terms of the corresponding or projected sates on the subnetworks and
the cut-vertex. A byproduct of this analysis is an alternative probabilistic
proof of the exactness of the closures for tree-like networks presented in
Sharkey et al. [13]. In this paper we also elaborate on how the main result can
be applied to more realistic networks, for which we write down the ODEs
explicitly and compare output from these to results from simulation.
Furthermore, we give a general, recipe-like method of how to apply the
reduction by closures technique for arbitrary networks, and give an upper bound
on the maximum number of equations needed for an exact representation.

27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph