dorsal/arxiv
View SchemaCluster approximations for probabilistic systems: a new perspective of epidemiological modelling
| Authors | Thomas Petermann, Paolo De Los Rios |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0401028 |
| URL | https://arxiv.org/abs/q-bio/0401028 |
| DOI | 10.1016/j.jtbi.2004.02.017 |
| Journal | J. Theor. Biol. 229, 1 (2004). |
Abstract
Especially in lattice structured populations, homogeneous mixing represents an inadequate assumption. Various improvements upon the ordinary pair approximation based on a number of assumptions concerning the higher-order correlations have been proposed. To find approaches that allow for a derivation of their dynamics remains a great challenge. By representing the population with its connectivity patterns as a homogeneous network, we propose a systematic methodology for the description of the epidemic dynamics that takes into account spatial correlations up to a desired range. The equations which the dynamical correlations are subject to, are derived in a straightforward way, and they are solved very efficiently due to their binary character. The method embeds very naturally spatial patterns such as the presence of loops characterizing the square lattice or the treelike structure ubiquitous in random networks, providing an improved description of the steady state as well as the invasion dynamics.
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"abstract": "Especially in lattice structured populations, homogeneous mixing represents\nan inadequate assumption. Various improvements upon the ordinary pair\napproximation based on a number of assumptions concerning the higher-order\ncorrelations have been proposed. To find approaches that allow for a derivation\nof their dynamics remains a great challenge. By representing the population\nwith its connectivity patterns as a homogeneous network, we propose a\nsystematic methodology for the description of the epidemic dynamics that takes\ninto account spatial correlations up to a desired range. The equations which\nthe dynamical correlations are subject to, are derived in a straightforward\nway, and they are solved very efficiently due to their binary character. The\nmethod embeds very naturally spatial patterns such as the presence of loops\ncharacterizing the square lattice or the treelike structure ubiquitous in\nrandom networks, providing an improved description of the steady state as well\nas the invasion dynamics.",
"arxiv_id": "q-bio/0401028",
"authors": [
"Thomas Petermann",
"Paolo De Los Rios"
],
"categories": [
"q-bio.PE",
"cond-mat.stat-mech",
"q-bio.QM"
],
"doi": "10.1016/j.jtbi.2004.02.017",
"journal_ref": "J. Theor. Biol. 229, 1 (2004).",
"title": "Cluster approximations for probabilistic systems: a new perspective of epidemiological modelling",
"url": "https://arxiv.org/abs/q-bio/0401028"
},
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