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Large-deviations of disease spreading dynamics with vaccination

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  • Yannick Feld
  • Alexander K Hartmann

Abstract

We numerically simulated the spread of disease for a Susceptible-Infected-Recovered (SIR) model on contact networks drawn from a small-world ensemble. We investigated the impact of two types of vaccination strategies, namely random vaccination and high-degree heuristics, on the probability density function (pdf) of the cumulative number C of infected people over a large range of its support. To obtain the pdf even in the range of probabilities as small as 10−80, we applied a large-deviation approach, in particular the 1/t Wang-Landau algorithm. To study the size-dependence of the pdfs within the framework of large-deviation theory, we analyzed the empirical rate function. To find out how typical as well as extreme mild or extreme severe infection courses arise, we investigated the structures of the time series conditioned to the observed values of C.

Suggested Citation

  • Yannick Feld & Alexander K Hartmann, 2023. "Large-deviations of disease spreading dynamics with vaccination," PLOS ONE, Public Library of Science, vol. 18(7), pages 1-22, July.
    • Handle: RePEc:plo:pone00:0287932
    DOI: 10.1371/journal.pone.0287932
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    References listed on IDEAS

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    2. A. Hartmann, 2011. "Large-deviation properties of largest component for random graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 84(4), pages 627-634, December.
    3. Hendrik Schawe & Alexander K. Hartmann, 2019. "Large-deviation properties of the largest biconnected component for random graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(4), pages 1-9, April.
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