title: 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.
authors.affiliation: Laboratory MAT-IRD, Department of Computer Science, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon. kouokam@yahoo.com
authors.forename: Etienne
authors.initials: E
authors.lastname: Kouokam
authors.forename: Pierre
authors.initials: P
authors.lastname: Auger
authors.forename: Hassan
authors.initials: H
authors.lastname: Hbid
authors.forename: Maurice
authors.initials: M
authors.lastname: Tchuente
mesh_terms: D008962:Models, Theoretical