空间结构化总体中的单个恢复与群集恢复
Individual versus cluster recoveries within a spatially structured population
摘要：
疾病动力学的随机建模有着悠久的传统。在第一个包含局部相互作用形式的空间结构的流行病模型中，有一个是接触过程。在这篇文章中，我们调查两个扩展的接触过程描述的过程中，一个单一的疾病在空间结构的人群分布在社会集群。也就是说，$d$维整数格的每个位点都被一群个体占据;每个个体可以是健康的或被感染的。疾病的演变取决于三个参数，即外部感染率，它模拟了集群之间的相互作用，内部感染率，它考虑了同一集群中个体之间的重复接触，以及每个社会集群的大小。对于第一个模型，我们假设集群恢复，而个人的恢复是假设为第二个。我们的目的是调查存在的非平凡的平稳分布这两个过程取决于每个三个参数的值。我们的研究结果表明，流行病的概率强烈依赖于恢复机制。
英文摘要：
Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the contact process describing the course of a single disease within a spatially structured human population distributed in social clusters. That is, each site of the $d$-dimensional integer lattice is occupied by a cluster of individuals; each individual can be healthy or infected. The evolution of the disease depends on three parameters, namely the outside infection rate which models the interactions between the clusters, the within infection rate which takes into account the repeated contacts between individuals in the same cluster, and the size of each social cluster. For the first model, we assume cluster recoveries, while individual recoveries are assumed for the second one. The aim is to investigate the existence of nontrivial stationary distributions for both processes depending on the value of each of the three parameters. Our results show that the probability of an epidemic strongly depends on the recovery mechanism.
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