Effect of the number of patches in a multi-patch SIRS model with fast migration on the basic reproduction rate

Etienne Kouokam 1, * Pierre Auger 2, 3, 4, * Hassan Hbid 5 Maurice Tchuente 1, 2, 3, 4, *
* Corresponding author
1 Laboratory MAT-IRD
2 IXXI - Institut Rhône-Alpin des systèmes complexes
3 GEODES - Modélisation mathématique et informatique de systèmes complexes naturels, biologiques ou sociaux
4 MASAIE - Tools and models of nonlinear control theory for epidemiology and immunology
LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
5 Department of Mathematics [Marroco]
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.
Keywords : SIRS model two patch system linear chain of patches fast migration aggregation of variables basic reproduction rate individual based model multi agent simulations
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Etienne Kouokam, Pierre Auger, Hassan Hbid, Maurice Tchuente. Effect of the number of patches in a multi-patch SIRS model with fast migration on the basic reproduction rate. Acta Biotheoretica, Springer Verlag, 2008, 56 (1-2), pp.75-86. ⟨10.1007/s10441-008-9036-y⟩. ⟨ird-00296726⟩

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