双尺度多型接触过程：空间显式集合种群的共存
Two-scale multitype contact process: coexistence in spatially explicit metapopulations
摘要：
已知接触过程的极限行为强烈地依赖于粒子在其上演化的图的几何形状：当规则格点上的接触过程仅表现出两个阶段时，齐次树上的过程表现出弱生存的中间阶段。同样，我们证明了图形的几何形状可以极大地影响多类型版本的接触过程的限制行为。也就是说，虽然人们强烈认为（并部分证明），多型接触过程的共存区域的规则格点减少到一个子集的相图与勒贝格测度为零，我们证明了共存区域的过程中，包括两个相互作用水平的图有一个积极的勒贝格测度。这种多尺度的空间随机过程的疾病动力学模型的相关性进行了讨论。
英文摘要：
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.
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