Effect of the Number of Patches in a Multi-patch SIRS Model with Fast Migration on the Basic Reproduction Rate |
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Authors: | Etienne Kouokam Pierre Auger Hassan Hbid Maurice Tchuente |
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Affiliation: | Laboratory MAT-IRD, Department of Computer Science, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon. kouokam@yahoo.com |
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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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