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

Two-scale multitype contact process: coexistence in spatially explicit metapopulations