Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections of all-to-all pair-wise interactions (cliques) and/or group interactions, involving many of their members at once. In this work, focusing on interaction structures represented as simplicial complexes, we present a discrete-time microscopic model of complex contagion for a susceptible-infected-susceptible dynamics. Introducing a particular edge clique cover and a heuristic to find it, the model accounts for the higher-order dynamical correlations among the members of the substructures (cliques/simplices). The analytical computation of the critical point reveals that higher-order correlations are responsible for its dependence on the higher-order couplings. While such dependence eludes any mean-field model, the possibility of a bi-stable region is extended to structured populations.

传染过程已被证明从根本上取决于传达它们的交互网络的结构特性。许多真实的网络系统的特点是集群子结构，代表所有对所有成对交互（集团）和/或组交互的集合，同时涉及许多成员。在这项工作中，我们专注于表示为单纯复合体的相互作用结构，我们提出了一个复杂传染的离散时间微观模型，用于易感感染易感动力学。引入特定的边缘集团覆盖和启发式来找到它，该模型解释了子结构（集团/单纯形）成员之间的高阶动态相关性。临界点的分析计算表明，高阶相关性是其对高阶耦合的依赖性的原因。虽然这种依赖性避开了任何平均场模型，但双稳态区域的可能性扩展到结构化种群。