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Mathematics of Epidemics on Networks pp 165–205Cite as

Mean-field approximations for heterogeneous networks

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Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 46))

Abstract

Section 4.5 showed that the homogeneous mean-field approximations cannot capture the system behaviour for networks with heterogeneous degree distributions. The heterogeneity in degree can significantly affect disease dynamics [254]. This requires more sophisticated models. In this chapter, we formulate mean-field models in terms of population-level counts of the number of nodes with a given degree and status.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Sussex, Falmer, Brighton, UK

    István Z. Kiss

  2. Applied Mathematics, Institute for Disease Modeling, Bellevue, WA, USA

    Joel C. Miller

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

    Péter L. Simon

Authors
  1. István Z. Kiss
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  2. Joel C. Miller
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  3. Péter L. Simon
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Kiss, I.Z., Miller, J.C., Simon, P.L. (2017). Mean-field approximations for heterogeneous networks. In: Mathematics of Epidemics on Networks. Interdisciplinary Applied Mathematics, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-50806-1_5

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