  It is known that the limiting behavior of the contact process strongly
depends upon the geometry of the graph on which particles evolve: while the
contact process on the regular lattice exhibits only two phases, the process on
homogeneous trees exhibits an intermediate phase of weak survival. Similarly,
we prove that the geometry of the graph can drastically affect the limiting
behavior of multitype versions of the contact process. Namely, while it is
strongly believed (and partly proved) that the coexistence region of the
multitype contact process on the regular lattice reduces to a subset of the
phase diagram with Lebesgue measure zero, we prove that the coexistence region
of the process on a graph including two levels of interaction has a positive
Lebesgue measure. The relevance of this multiscale spatial stochastic process
as a model of disease dynamics is also discussed.
