标题： 两尺度多类型接触过程：空间明确的集合种群中的共存 显示英文标题

标题： 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依赖于粒子演化的图的几何结构：虽然在规则格子上的接触过程仅表现出两种相，而在均匀树上的过程则表现出一种中间的弱生存相。 类似地，我们证明了图的几何结构可以极大地影响多类型接触过程的极限行为。 具体来说，尽管人们普遍认为（并部分证明了）在规则格子上的多类型接触过程的共存区域仅是相图中勒贝格测度为零的子集，但我们证明了包含两个相互作用层次的图上的过程的共存区域具有正的勒贝格测度。 这种多尺度空间随机过程作为疾病动力学模型的相关性也进行了讨论。 显示英文摘要

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.