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Percolation and the pandemic

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  • Ziff, Robert M.

Abstract

This paper is dedicated to the memory of Dietrich Stauffer, who was a pioneer in percolation theory and applications of it to problems of society, such as epidemiology. An epidemic is a percolation process gone out of control, that is, going beyond the critical transition threshold pc. Here we discuss how the threshold is related to the basic infectivity of neighbors R0, for trees (Bethe lattice), trees with triangular cliques, and in non-planar lattice percolation with extended-range connectivity. It is shown how having a smaller range of contacts increases the critical value of R0 above the value R0,c=1 appropriate for a tree, an infinite-range system, or a large completely connected graph.

Suggested Citation

  • Ziff, Robert M., 2021. "Percolation and the pandemic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    • Handle: RePEc:eee:phsmap:v:568:y:2021:i:c:s0378437120310219
    DOI: 10.1016/j.physa.2020.125723
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    Cited by:

    1. Balankin, Alexander S., 2024. "A survey of fractal features of Bernoulli percolation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    2. Campi, Gaetano & Bianconi, Antonio, 2022. "Periodic recurrent waves of Covid-19 epidemics and vaccination campaign," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Malarz, Krzysztof, 2023. "Random site percolation thresholds on square lattice for complex neighborhoods containing sites up to the sixth coordination zone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    4. Katori, Machiko & Katori, Makoto, 2021. "Continuum percolation and stochastic epidemic models on Poisson and Ginibre point processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    5. Yann Lucas Silva & Ariadne Andrade Costa, 2024. "Periodic boundary condition effects in small-world networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(7), pages 1-9, July.

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