 
Summary: Fields Institute Communications
Volume 00, 0000
Disease Spread in Metapopulations
Julien Arino
Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2,
arinoj@cc.umanitoba.ca
P. van den Driessche
Department of Mathematics and Statistics, University of Victoria, B.C., Canada V8W 3P4,
pvdd@math.uvic.ca
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
