Recent research on social contagion processes has revealed the limitations of traditional networks, which capture only pairwise relationships, to characterize complex multiparty relationships and group influences properly. Social contagion processes on higher-order networks (simplicial complexes and general hypergraphs) have therefore emerged as a novel frontier. In this work, we investigate discrete-time Susceptible-Infected-Susceptible (SIS) social contagion processes occurring on weighted and directed hypergraphs and their extensions to bivirus cases and general higher-order SIS processes with the aid of tensor algebra. Our focus lies in comprehensively characterizing the healthy state and endemic equilibria within this framework. The emergence of bistability or multistability behavior phenomena, where multiple equilibria coexist and are simultaneously locally asymptotically stable, is demonstrated in view of the presence of the higher-order interaction. The novel sufficient conditions of the appearance for system behaviors, which are determined by both (higher-order) network topology and transition rates, are provided to assess the likelihood of the SIS social contagion processes causing an outbreak. More importantly, given the equilibrium is locally stable, an explicit domain of attraction associated with the system parameters is constructed. Moreover, a learning method to estimate the transition rates is presented. In the end, the attained theoretical results are supplemented via numerical examples. Specifically, we evaluate the effectiveness of the networked SIS social contagion process by comparing it with the $2^n$-state Markov chain model. These numerical examples are given to highlight the performance of parameter learning algorithms and the system behaviors of the discrete-time SIS social contagion process.
Effects of higher-order interactions and homophily on information access inequality
Northeastern University（东北大学）；Complexity Science Hub Vienna（维也纳复杂科学中心）；Khoury College of Computer Sciences, Northeastern University（东北大学库里计算机科学学院）；Santa Fe Institute（圣塔菲研究所）
Reducing Recurrent Competitive Epidemics via Dynamic Resource Allocation
Centre Borelli, ENS Paris-Saclay, CNRS（博雷利中心，巴黎萨克雷高等师范学院，法国国家科学研究中心）；School of Computer Science and Applied Mathematics, University of the Witwatersrand（威特沃特斯兰德大学计算机科学与应用数学学院）
Adaptive Epidemic Dynamics on Hypergraphs with Group-Level Immunization and Rewiring
College of Artificial Intelligence, Southwest University（西南大学人工智能学院）；School of Systems Science/Institute of Nonequilibrium Systems, Beijing Normal University（北京师范大学系统科学学院/非平衡系统研究所）；Business College, Southwest University（西南大学商学院）；Faculty of Natural Sciences and Mathematics, University of Maribor（马里博尔大学自然科学与数学学院）；Community Healthcare Center Dr. Adolf Drolc Maribor（马里博尔阿道夫·德罗尔博士社区健康中心）；Department of Physics, Kyung Hee University（庆熙大学物理系）；University College, Korea University（高丽大学大学院）
