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

TL;DR

This paper demonstrates that the geometry of the underlying graph significantly influences the coexistence of multiple types in a multitype contact process, especially on multiscale spatial structures, unlike on regular lattices.

Contribution

It proves that multiscale graph structures can support a positive measure of coexistence regions in multitype contact processes, contrasting with the negligible coexistence on regular lattices.

Findings

Coexistence region has positive Lebesgue measure on multiscale graphs.

Geometry drastically affects the limiting behavior of multitype contact processes.

Multiscale structures can sustain coexistence unlike regular lattices.

Abstract

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.