Two-scale Multitype Contact Process: Coexistence in Spatially Explicit Metapopulations
2011, v.17, №2, 151-186
It is known from past research 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 regular lattices exhibits only two phases, the process on homogeneous trees exhibits an intermediate phase of weak survival. Similarly, we prove that the geometry of the interaction network can drastically affect the limiting behavior of multitype versions of the contact process as well. Namely, while it is strongly believed (and partly proved) that the coexistence region of the multitype contact process on regular lattices 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 measure. This result is somewhat reminiscent of a recent result of Cox and Schinazi. However, whereas their analysis focuses on multitype contact processes on regular trees, our results apply to biologically realistic stochastic models, which therefore gives a better understanding of the mechanisms that promote coexistence in ecological communities. In particular, the relevance of the two-scale multitype contact process as a model of disease dynamics is also discussed.
Keywords: interacting particle systems,multitype contact process,coexistence,multiscale argument,oriented percolation,metapopulation,disease dynamics,tumor cells