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

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.
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Acta Biotheoretica, Springer Verlag, 2008, 56 (1-2), pp.75-86. 〈10.1007/s10441-008-9036-y〉
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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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