%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Kouokam, E.
%A Auger, Pierre
%A Hbid, H.
%A Tchuente, Maurice
%T Effect of the number of patches in a multi-patch SIRS model with fast migration on the basic reproduction rate
%D 2008
%L fdi:010042615
%G ENG
%J Acta Biotheoretica
%@ 0001-5342
%K SIRS model ; two patch system ; linear chain of patches ; fast migration ; aggregation of variables ; basic reproduction rate ; individual based model ; multi agent simulations
%M CC:0002563379-0005
%N 1-2
%P 75-86
%R 10.1007/s10441-008-9036-y
%U https://www.documentation.ird.fr/hor/fdi:010042615
%> https://www.documentation.ird.fr/intranet/publi/2008/06/010042615.pdf
%V 56
%W Horizon (IRD)
%X 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.
%$ 050 ; 020