The effect of heterogeneity on hypergraph contagion models

The dynamics of network social contagion processes such as opinion formation and epidemic spreading are often mediated by interactions between multiple nodes. Previous results have shown that these higher-order interactions can profoundly modify the dynamics of contagion processes, resulting in bistability, hysteresis, and explosive transitions. In this paper, we present and analyze a hyperdegree-based mean-field description of the dynamics of the susceptible–infected–susceptible model on hypergraphs, i.e., networks with higher-order interactions, and illustrate its applicability with the example of a hypergraph where contagion is mediated by both links (pairwise interactions) and triangles (three-way interactions). We consider various models for the organization of link and triangle structures and different mechanisms of higher-order contagion and healing. We find that explosive transitions can be suppressed by heterogeneity in the link degree distribution when links and triangles are chosen independently or when link and triangle connections are positively correlated when compared to the uncorrelated case. We verify these results with microscopic simulations of the contagion process and with analytic predictions derived from the mean-field model. Our results show that the structure of higher-order interactions can have important effects on contagion processes on hypergraphs.

[1]  B. Kahng,et al.  Simplicial SIS model in scale-free uniform hypergraph , 2019 .

[2]  Ginestra Bianconi,et al.  Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes. , 2016, Physical review. E.

[3]  A. Baronchelli,et al.  Experimental evidence for tipping points in social convention , 2018, Science.

[4]  Pedro Cisneros-Velarde,et al.  Multi-group SIS Epidemics with Simplicial and Higher-Order Interactions , 2020, ArXiv.

[5]  Alessandro Vespignani,et al.  Modeling the spatial spread of infectious diseases: The GLobal Epidemic and Mobility computational model , 2010, J. Comput. Sci..

[6]  Yun Liu,et al.  Opinion formation on social media: an empirical approach. , 2014, Chaos.

[7]  Robin Cowan,et al.  Network Structure and the Diffusion of Knowledge , 2004 .

[8]  Jean-Gabriel Young,et al.  Networks beyond pairwise interactions: structure and dynamics , 2020, ArXiv.

[9]  Eamonn B. Mallon,et al.  Quorum sensing, recruitment, and collective decision-making during colony emigration by the ant Leptothorax albipennis , 2002, Behavioral Ecology and Sociobiology.

[10]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[11]  D. Meadows-Klue.  The Tipping Point: How Little Things Can Make a Big Difference , 2004 .

[12]  Jean-Gabriel Young,et al.  Construction of and efficient sampling from the simplicial configuration model. , 2017, Physical review. E.

[13]  Jonathan Touboul,et al.  The hipster effect: When anti-conformists all look the same , 2014, Discrete & Continuous Dynamical Systems - B.

[14]  Antoine Allard,et al.  School closures, event cancellations, and the mesoscopic localization of epidemics in networks with higher-order structure , 2020, 2003.05924.

[15]  Gyula Y Katona,et al.  SIS Epidemic Propagation on Hypergraphs , 2015, Bulletin of Mathematical Biology.

[16]  Joel C. Miller,et al.  Stochasticity and heterogeneity in the transmission dynamics of SARS-CoV-2 , 2020, 2005.13689.

[17]  D. Watts,et al.  Influentials, Networks, and Public Opinion Formation , 2007 .

[18]  Ginestra Bianconi,et al.  Explosive higher-order Kuramoto dynamics on simplicial complexes , 2019, Physical review letters.

[19]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Yamir Moreno,et al.  Social contagion models on hypergraphs , 2020, Physical Review Research.

[21]  J. Gómez-Gardeñes,et al.  A mathematical model for the spatiotemporal epidemic spreading of COVID19 , 2020, medRxiv.

[22]  J. Grilli,et al.  Higher-order interactions stabilize dynamics in competitive network models , 2017, Nature.

[23]  Jon M. Kleinberg,et al.  Simplicial closure and higher-order link prediction , 2018, Proceedings of the National Academy of Sciences.

[24]  Vito Latora,et al.  Simplicial models of social contagion , 2018, Nature Communications.

[25]  Jesús Gómez-Gardeñes,et al.  Annealed and mean-field formulations of disease dynamics on static and adaptive networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Christian Kuehn,et al.  Adaptive voter model on simplicial complexes. , 2020, Physical review. E.

[27]  Christos Faloutsos,et al.  Epidemic spreading in real networks: an eigenvalue viewpoint , 2003, 22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings..

[28]  Thomas House,et al.  Modelling epidemics on networks , 2011, 1111.4875.

[29]  R. Pastor-Satorras,et al.  Epidemic spreading in correlated complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[31]  P. Trapman,et al.  On analytical approaches to epidemics on networks. , 2007, Theoretical population biology.

[32]  Yamir Moreno,et al.  Phase transitions and stability of dynamical processes on hypergraphs , 2020, Communications Physics.

[33]  Joel C Miller,et al.  Edge-based compartmental modelling for infectious disease spread , 2011, Journal of The Royal Society Interface.

[34]  A. Arenas,et al.  Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplexes. , 2019, Physical review letters.

[35]  Alex Arenas,et al.  Abrupt phase transition of epidemic spreading in simplicial complexes , 2020 .

[36]  M. Newman.  Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  P. S. Skardal,et al.  Bifurcation analysis and structural stability of simplicial oscillator populations , 2020 .

[38]  Pradumn Kumar Pandey,et al.  A model for the spread of an epidemic from local to global: A case study of COVID-19 in India , 2020, ArXiv.

[39]  Paul J. B. Hart,et al.  Quorum decision-making facilitates information transfer in fish shoals , 2008, Proceedings of the National Academy of Sciences.