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Contagion dynamics on higher-order networks

Nature Reviews Physics (2024)Cite this article

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Abstract

A paramount research challenge in network and complex systems science is to understand the dissemination of diseases, information and behaviour. The COVID-19 pandemic and the proliferation of misinformation are examples that highlight the importance of these dynamic processes. In recent years, it has become clear that studies of higher-order networks may unlock new avenues for investigating such processes. Despite being in its early stages, the examination of social contagion in higher-order networks has witnessed a surge of research and concepts, revealing different functional forms for the spreading dynamics and offering novel insights. This Review presents a focused overview of this body of literature and proposes a unified formalism that covers most of these forms. The goal is to underscore the similarities and distinctions among various models to motivate further research on the general and universal properties of such models. We also highlight that although the path for additional theoretical exploration appears clear, the empirical validation of these models through data or experiments remains scant, with an unsettled roadmap as of today. We therefore conclude with some perspectives aimed at providing possible research directions that could contribute to a better understanding of this class of dynamical processes, both from a theoretical and a data-oriented point of view.

Key points

  • Contagion models in higher-order systems are motivated by problems relating to social interactions and to epidemics. There are various models and their interpretation changes depending on the context, but their mathematical formulation is similar and many models share key features and behaviours.

  • Identifying these general and specific properties of models will improve our understanding of higher-order systems as a whole. In this Review, we propose a unified formalism that covers most of the models in the literature.

  • Neglecting higher-order effects could completely change the process. For example, a discontinuous transition in a higher-order system could be perceived as continuous in a projected pairwise system.

  • Data validation and social experiments on a large scale are still lacking. Although there are structural data for some systems, for many dynamical processes data remain insufficient.

  • The study of contagion models in higher-order systems is an inherently interdisciplinary endeavour, in which physics and mathematics can provide new insights and interpretations for social sciences and epidemiology, among others.

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Fig. 1: Different types of interactions in higher-order networks.
Fig. 2: Susceptible–infected–susceptible prevalence ρ in the pairwise case according to the most common approaches.

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Acknowledgements

A.A. acknowledges support through the grant RYC2021-033226-I funded by MCIN/AEI/10.13039/501100011033 and the European Union ‘NextGenerationEU/PRTR’. Y.M. was partially supported by the Government of Aragón, Spain, and ‘ERDF — a way of making Europe’ through grant E36-23R (FENOL) and by Ministerio de Ciencia e Innovación, Agencia Española de Investigación (MCIN/AEI/10.13039/501100011033) grant no. PID2020-115800GB-I00.

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  1. CENTAI Institute, Turin, Italy

    Guilherme Ferraz de Arruda & Yamir Moreno

  2. Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza, Spain

    Alberto Aleta & Yamir Moreno

  3. Department of Theoretical Physics, Faculty of Sciences, University of Zaragoza, Zaragoza, Spain

    Alberto Aleta & Yamir Moreno

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Ferraz de Arruda, G., Aleta, A. & Moreno, Y. Contagion dynamics on higher-order networks. Nat Rev Phys (2024). https://doi.org/10.1038/s42254-024-00733-0

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