Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-field models for non-Markovian epidemics on networks: from
  edge-based compartmental to pairwise models   This paper presents a novel extension of the edge-based compartmental model
for epidemics with arbitrary distributions of transmission and recovery times.
Using the message passing approach we also derive a new pairwise-like model for
epidemics with Markovian transmission and an arbitrary recovery period. The new
pairwise-like model allows one to formally prove that the message passing and
edge-based compartmental models are equivalent in the case of Markovian
transmission and arbitrary recovery processes. The edge-based and message
passing models are conjectured to also be equivalent for arbitrary transmission
processes; we show the first step of a full proof of this. The new
pairwise-like model encompasses many existing well-known models that can be
obtained by appropriate reductions. It is also amenable to a relatively
straightforward numerical implementation. We test the theoretical results by
comparing the numerical solutions of the various pairwise-like models to
results based on explicit stochastic network simulations.

16
The categories of this paper are: stat
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg