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Epidemic thresholds identification of susceptible-infected-recovered model based on the Eigen Microstate

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  • Wang, Ning-Ning
  • Qiu, Shui-Han
  • Zhong, Xiao Wen
  • Di, Zeng-Ru

Abstract

Epidemic threshold estimation plays a critical role in prevention strategies. Besides theoretical methods, some numerical methods estimate the threshold through the scale divergence of outbreak size near critical state. But the bimodal distribution of outbreak size may make the estimated threshold higher. In this paper, we extend the Eigen Microstate (EM) method to the susceptible-infected-recovered (SIR) epidemic model and devise the eigen measure to estimate the threshold using the scale divergence of singular values. Compared with the susceptibility and variability measure, the estimated threshold of eigen measure is closer to the theoretical results of the heterogeneous mean-field (HMF) and the quenched mean-field (QMF). In addition, better than the assortativity coefficient, network mean degree or dimension has a more significant effect on estimation accuracy. Under complex epidemic mechanisms, such as periodic time-varying networks and migration between networked populations, the threshold estimation of QMF models indicates that the eigen measure is more stable and accurate than the other two measures. Combined with renormalization group theory, our method may have practical significance in megalopolis epidemic warning.

Suggested Citation

  • Wang, Ning-Ning & Qiu, Shui-Han & Zhong, Xiao Wen & Di, Zeng-Ru, 2023. "Epidemic thresholds identification of susceptible-infected-recovered model based on the Eigen Microstate," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    • Handle: RePEc:eee:apmaco:v:449:y:2023:i:c:s0096300323000930
    DOI: 10.1016/j.amc.2023.127924
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    References listed on IDEAS

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    1. Hong, Xiao & Han, Yuexing & Wang, Bing, 2023. "Impacts of detection and contact tracing on the epidemic spread in time-varying networks," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    2. Wang, Ning-Ning & Jin, Zhen & Wang, Ya-Jing & Di, Zeng-Ru, 2020. "Epidemics spreading in periodic double layer networks with dwell time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. Liu, Li & Luo, Xiaofeng & Chang, Lili, 2017. "Vaccination strategies of an SIR pair approximation model with demographics on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 282-290.
    4. Martin Rypdal & George Sugihara, 2019. "Inter-outbreak stability reflects the size of the susceptible pool and forecasts magnitudes of seasonal epidemics," Nature Communications, Nature, vol. 10(1), pages 1-8, December.
    5. Zhu, Xuzhen & Liu, Yuxin & Wang, Shengfeng & Wang, Ruijie & Chen, Xiaolong & Wang, Wei, 2021. "Allocating resources for epidemic spreading on metapopulation networks," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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