具有社会簇和无症状状态的接触过程
The contact process with social clusters and asymptomatic states
AI总结：
本文研究接触过程的变体，在每个格点放置社会簇并区分有症状与无症状个体，证明确定性平均场与随机空间模型在四个感染率下具有相同相变，并发现簇大小可独立驱动相变。
AI中文摘要：
本文关注接触过程的一个自然变体，该变体在每个格点放置一个由个体组成的社会簇，而非单个个体，并区分有症状个体与无症状个体。具体而言，该流行病模型依赖于四个感染参数：有症状和无症状个体的外部（簇间）感染率和内部（簇内）感染率。新感染的个体最初为无症状状态，随后以自发突变率转变为有症状状态，而感染个体以基线速率1恢复。我们研究了当每个簇缩减为一对个体时确定性非空间平均场模型的相结构，并证明了随机空间模型对所有簇大小在这四个感染率方面表现出相同的相变。我们还证明了空间模型中由簇大小本身驱动的相变的存在性。
英文摘要：
This paper is concerned with a natural variant of the contact process that places a social cluster of individuals, rather than a single individual, at each lattice point, and distinguishes between symptomatic and asymptomatic individuals. In particular, the epidemic model depends on four infection parameters: the external (inter-cluster) and internal (intra-cluster) infection rates for both symptomatic and asymptomatic individuals. Newly infected individuals begin as asymptomatic before transitioning to the symptomatic state at a spontaneous mutation rate, and infected individuals recover at a baseline rate of one. We study the phase structure of the deterministic nonspatial mean-field model when each cluster reduces to a pair of individuals, and prove that the stochastic spatial model exhibits the same phase transitions with respect to the four infection rates for all cluster sizes. We also prove the existence of a phase transition driven by the cluster size itself for the spatial model.
