Diseases in metapopulations
Department of Mathematics, University of Manitoba,
Winnipeg, Manitoba R3T 2N2, Canada.
Metapopulation models consist of graphs, with systems of dif-
ferential equations at each vertex. This modeling paradigm is
appropriate for the description of the spatio-temporal spread of
infectious diseases. In this document, I present the setting of
these models, and some of the mathematical techniques that can
be used to study them. I conclude with a brief review of some
models using this approach.
1 Foreword Notation
These lecture notes attempt to give a relatively exhaustive overview of
methodological aspects of ordinary differential equations metapopulation
models in the context of the spatial spread of diseases. They are based on
work carried out with Pauline van den Driessche (in particular [5, 6, 7, 8])
and extensions of this work, and the work of all the authors cited.