dorsal/arxiv
View SchemaNetwork-based analysis of stochastic SIR epidemic models with random and proportionate mixing
| Authors | Eben Kenah, James M. Robins |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0702027 |
| URL | https://arxiv.org/abs/q-bio/0702027 |
| DOI | 10.1016/j.jtbi.2007.09.011 |
| Journal | Journal of Theoretical Biology 249: 706-722, December 2007 |
Abstract
In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic SIR epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because undirected edges disappear in the limit of a large population. In a series of simulations, we show that epidemic percolation networks accurately predict the mean outbreak size and probability and final size of an epidemic for a variety of epidemic models in homogeneous and heterogeneous populations. Finally, we show that epidemic percolation networks can be used to re-derive classical results from several different areas of infectious disease epidemiology. In an appendix, we show that an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model in a closed population and prove that the distribution of outbreak sizes given the infection of any given node in the SIR model is identical to the distribution of its out-component sizes in the corresponding probability space of epidemic percolation networks. We conclude that the theory of percolation on semi-directed networks provides a very general framework for the analysis of stochastic SIR models in closed populations.
{
"annotation_id": "986a75bb-67df-41c8-b44e-4837f8066675",
"date_created": "2026-03-02T18:01:35.805000Z",
"date_modified": "2026-03-02T18:01:35.805000Z",
"file_hash": "40f95346d7d4f7f4209fdd92b1d66b7d5bb98d3d8d9a1f735c3167e5dcd1a790",
"private": false,
"record": {
"abstract": "In this paper, we outline the theory of epidemic percolation networks and\ntheir use in the analysis of stochastic SIR epidemic models on undirected\ncontact networks. We then show how the same theory can be used to analyze\nstochastic SIR models with random and proportionate mixing. The epidemic\npercolation networks for these models are purely directed because undirected\nedges disappear in the limit of a large population. In a series of simulations,\nwe show that epidemic percolation networks accurately predict the mean outbreak\nsize and probability and final size of an epidemic for a variety of epidemic\nmodels in homogeneous and heterogeneous populations. Finally, we show that\nepidemic percolation networks can be used to re-derive classical results from\nseveral different areas of infectious disease epidemiology. In an appendix, we\nshow that an epidemic percolation network can be defined for any\ntime-homogeneous stochastic SIR model in a closed population and prove that the\ndistribution of outbreak sizes given the infection of any given node in the SIR\nmodel is identical to the distribution of its out-component sizes in the\ncorresponding probability space of epidemic percolation networks. We conclude\nthat the theory of percolation on semi-directed networks provides a very\ngeneral framework for the analysis of stochastic SIR models in closed\npopulations.",
"arxiv_id": "q-bio/0702027",
"authors": [
"Eben Kenah",
"James M. Robins"
],
"categories": [
"q-bio.QM",
"cond-mat.stat-mech",
"math.PR"
],
"doi": "10.1016/j.jtbi.2007.09.011",
"journal_ref": "Journal of Theoretical Biology 249: 706-722, December 2007",
"title": "Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing",
"url": "https://arxiv.org/abs/q-bio/0702027"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "a22cf74c-6f84-4eb4-acf1-445b8654e869",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}