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Insights from exact social contagion dynamics on networks with higher-order structures

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Title: Insights from exact social contagion dynamics on networks with higher-order structures
Authors: Kiss, István Z., Iacopini, Iacopo, Simon, Péter L., Georgiou, Nicos
Publication Year: 2023
Collection: Mathematics
Physics (Other)
Quantitative Biology
Subject Terms: Physics - Physics and Society, Mathematics - Dynamical Systems, Mathematics - Probability, Quantitative Biology - Populations and Evolution
More Details: Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or heuristically derived epidemic spreading models it was shown that new phenomena can emerge, such as bi-stability/multistability. Here, we show that such new emerging phenomena do not require complex contact patterns, such as community structures, but naturally result from the higher-order contagion mechanisms. We show this by deriving an exact higher-order SIS model and its limiting mean-field equivalent for fully connected simplicial complexes. Going beyond previous results, we also give the global bifurcation picture for networks with 3- and 4-body interactions, with the latter allowing for two non-trivial stable endemic steady states. Differently from previous approaches, we are able to study systems featuring interactions of arbitrary order. In addition, we characterise the contributions from higher-order infections to the endemic equilibrium as perturbations of the pairwise baseline, finding that these diminish as the pairwise rate of infection increases. Our approach represents a first step towards a principled understanding of higher-order contagion processes beyond triads and opens up further directions for analytical investigations.
Comment: 19 pages, 14 figures
Document Type: Working Paper
Access URL: http://arxiv.org/abs/2309.12752
Accession Number: edsarx.2309.12752
Database: arXiv
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  Data: Insights from exact social contagion dynamics on networks with higher-order structures
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  Data: <searchLink fieldCode="AR" term="%22Kiss%2C+István+Z%2E%22">Kiss, István Z.</searchLink><br /><searchLink fieldCode="AR" term="%22Iacopini%2C+Iacopo%22">Iacopini, Iacopo</searchLink><br /><searchLink fieldCode="AR" term="%22Simon%2C+Péter+L%2E%22">Simon, Péter L.</searchLink><br /><searchLink fieldCode="AR" term="%22Georgiou%2C+Nicos%22">Georgiou, Nicos</searchLink>
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  Data: 2023
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  Data: Mathematics<br />Physics (Other)<br />Quantitative Biology
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  Data: Recently there has been an increasing interest in studying dynamical processes on networks exhibiting higher-order structures, such as simplicial complexes, where the dynamics acts above and beyond dyadic interactions. Using simulations or heuristically derived epidemic spreading models it was shown that new phenomena can emerge, such as bi-stability/multistability. Here, we show that such new emerging phenomena do not require complex contact patterns, such as community structures, but naturally result from the higher-order contagion mechanisms. We show this by deriving an exact higher-order SIS model and its limiting mean-field equivalent for fully connected simplicial complexes. Going beyond previous results, we also give the global bifurcation picture for networks with 3- and 4-body interactions, with the latter allowing for two non-trivial stable endemic steady states. Differently from previous approaches, we are able to study systems featuring interactions of arbitrary order. In addition, we characterise the contributions from higher-order infections to the endemic equilibrium as perturbations of the pairwise baseline, finding that these diminish as the pairwise rate of infection increases. Our approach represents a first step towards a principled understanding of higher-order contagion processes beyond triads and opens up further directions for analytical investigations.<br />Comment: 19 pages, 14 figures
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RecordInfo BibRecord:
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    Subjects:
      – SubjectFull: Physics - Physics and Society
        Type: general
      – SubjectFull: Mathematics - Dynamical Systems
        Type: general
      – SubjectFull: Mathematics - Probability
        Type: general
      – SubjectFull: Quantitative Biology - Populations and Evolution
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      – TitleFull: Insights from exact social contagion dynamics on networks with higher-order structures
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            NameFull: Iacopini, Iacopo
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            NameFull: Simon, Péter L.
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            NameFull: Georgiou, Nicos
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              Type: published
              Y: 2023
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