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SIS Epidemic Propagation on Hypergraphs

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Abstract

Mathematical modelling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact master equations of the propagation process are derived for an arbitrary hypergraph given by its incidence matrix. Based on these, moment closure approximation and mean-field models are introduced and compared to individual-based stochastic simulations. The simulation algorithm, developed for networks, is extended to hypergraphs. The effects of hypergraph structure and the model parameters are investigated via individual-based simulation results.

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Acknowledgments

Péter L. Simon acknowledges support from Hungarian Scientific Research Fund, OTKA, (Grant No. 115926). Gyula Y. Katona acknowledges support from OTKA (Grant No. 108947 and 116769).

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Authors and Affiliations

  1. Institute of Mathematics, Eötvös Loránd University Budapest, Budapest, Hungary

    Ágnes Bodó & Péter L. Simon

  2. Numerical Analysis and Large Networks Research Group, Hungarian Academy of Sciences, Budapest, Hungary

    Ágnes Bodó, Gyula Y. Katona & Péter L. Simon

  3. Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, Hungary

    Gyula Y. Katona

Authors
  1. Ágnes Bodó
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  2. Gyula Y. Katona
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  3. Péter L. Simon
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Correspondence to Péter L. Simon.

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Bodó, Á., Katona, G.Y. & Simon, P.L. SIS Epidemic Propagation on Hypergraphs. Bull Math Biol 78, 713–735 (2016). https://doi.org/10.1007/s11538-016-0158-0

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  • DOI: https://doi.org/10.1007/s11538-016-0158-0

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