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Fields Institute Communications Volume 00, 0000

Summary: Fields Institute Communications
Volume 00, 0000
Disease Spread in Metapopulations
Julien Arino
Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2,
P. van den Driessche
Department of Mathematics and Statistics, University of Victoria, B.C., Canada V8W 3P4,
Abstract. Some continuous time, discrete space, metapopulation mod-
els that have been formulated for disease spread are presented. Motiva-
tion for such a formulation with travel between discrete patches is pre-
sented. A system of 4p ordinary dierential equations describes disease
spread in an environment divided into p patches. The basic reproduc-
tion number R0 is calculated, with the disease dying out in each patch
if R0 < 1. If travel is assumed to be independent of disease status, then
numerical results are cited that indicate that for R0 > 1 solutions tend
to an endemic equilibrium with the disease present in each patch. The
system is extended to include cross infection between several species. A
second extension involves keeping track of both the current patch and


Source: Arino, Julien - Department of Mathematics, University of Manitoba


Collections: Mathematics