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Effect of the Number of Patches in a Multi-patch SIRS Model with Fast Migration on the Basic Reproduction Rate

Effect of the Number of Patches in a Multi-patch SIRS Model with Fast Migration on the Basic... We consider a two-patch epidemiological system where individuals can move from one patch to another, and local interactions between the individuals within a patch are governed by the classical SIRS model. When the time-scale associated with migration is much smaller than the time-scale associated with infection, aggregation methods can be used to simplify the initial complete model formulated as a system of ordinary differential equations. Analysis of the aggregated model then shows that the two-patch basic reproduction rate is smaller than the 1 patch one. We extend this result to a linear chain of P patches (P > 2). These results are illustrated by some examples for which numerical integration of the system of ordinary differential equations is performed. Simulations of an individual based model implemented with a multi-agent system are also carried out. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

Effect of the Number of Patches in a Multi-patch SIRS Model with Fast Migration on the Basic Reproduction Rate

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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media B.V.
Subject
Philosophy; Evolutionary Biology; Philosophy of Biology
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/s10441-008-9036-y
pmid
18273682
Publisher site
See Article on Publisher Site

Abstract

We consider a two-patch epidemiological system where individuals can move from one patch to another, and local interactions between the individuals within a patch are governed by the classical SIRS model. When the time-scale associated with migration is much smaller than the time-scale associated with infection, aggregation methods can be used to simplify the initial complete model formulated as a system of ordinary differential equations. Analysis of the aggregated model then shows that the two-patch basic reproduction rate is smaller than the 1 patch one. We extend this result to a linear chain of P patches (P > 2). These results are illustrated by some examples for which numerical integration of the system of ordinary differential equations is performed. Simulations of an individual based model implemented with a multi-agent system are also carried out.

Journal

Acta BiotheoreticaSpringer Journals

Published: Feb 14, 2008

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