Most mathematical models introduced in the biological literature that
describe inherently spatial phenomena of interacting
populations consist of systems of ordinary differential equations, thus
leaving out any spatial structure. The spatial
component, however, is identified as an important factor in how
communities are shaped, and spatial models can result in
predictions that differ from non-spatial models. The aim of my research
is to understand the role of space in ecology,
epidemiology and population genetics through the mathematical analysis of
a class of stochastic processes known as interacting
particle systems. These processes are ideally suited to investigate the
consequences of the inclusion of a spatial
structure in the form of stochastic and local interactions. This includes
generalizations of the contact process and the
voter model in spatially heterogeneous environments and on inhomogeneous
graphs.
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