dorsal/arxiv
View SchemaPair Approximation Models for Disease Spread
| Authors | Jerome Benoit, Ana Nunes, Margarida Telo da Gama |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0510005 |
| URL | https://arxiv.org/abs/q-bio/0510005 |
| DOI | 10.1140/epjb/e2006-00096-x |
| Journal | Eur. Phys. J. B 50 (2006), no. 1-2, 177--181 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We consider a Susceptible-Infective-Recovered (SIR) model, where the mechanism for the renewal of susceptibles is demographic, on a ring with next nearest neighbour interactions, and a family of correlated pair approximations (CPA), parametrized by a measure of the relative contributions of loops and open triplets of the sites involved in the infection process. We have found that the phase diagram of the CPA, at fixed coordination number, changes qualitatively as the relative weight of the loops increases, from the phase diagram of the uncorrelated pair approximation to phase diagrams typical of one-dimensional systems. In addition, we have performed computer simulations of the same model and shown that while the CPA with a constant correlation parameter cannot describe the global behaviour of the model, a reasonable description of the endemic equilibria as well as of the phase diagram may be obtained by allowing the parameter to depend on the demographic rate.
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"abstract": "We consider a Susceptible-Infective-Recovered (SIR) model, where the\nmechanism for the renewal of susceptibles is demographic, on a ring with next\nnearest neighbour interactions, and a family of correlated pair approximations\n(CPA), parametrized by a measure of the relative contributions of loops and\nopen triplets of the sites involved in the infection process. We have found\nthat the phase diagram of the CPA, at fixed coordination number, changes\nqualitatively as the relative weight of the loops increases, from the phase\ndiagram of the uncorrelated pair approximation to phase diagrams typical of\none-dimensional systems. In addition, we have performed computer simulations of\nthe same model and shown that while the CPA with a constant correlation\nparameter cannot describe the global behaviour of the model, a reasonable\ndescription of the endemic equilibria as well as of the phase diagram may be\nobtained by allowing the parameter to depend on the demographic rate.",
"arxiv_id": "q-bio/0510005",
"authors": [
"Jerome Benoit",
"Ana Nunes",
"Margarida Telo da Gama"
],
"categories": [
"q-bio.PE"
],
"doi": "10.1140/epjb/e2006-00096-x",
"journal_ref": "Eur. Phys. J. B 50 (2006), no. 1-2, 177--181",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Pair Approximation Models for Disease Spread",
"url": "https://arxiv.org/abs/q-bio/0510005"
},
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