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Uncovering self-similar patterns in infectious disease transmission trees: Development of a Bayesian Connectivity Algorithm

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  • Wang, Cheng-Hua
  • Wen, Tzai-Hung

Abstract

Epidemic dynamics are effectively modeled using tree structures that represent the transmission pathways of infectious diseases. Analyzing these transmission trees offers key insights into the mechanisms driving power-law growth, especially in the early stages of an outbreak. However, the degree of self-similarity within these trees remains insufficiently understood. This study introduces a Bayesian Connectivity Algorithm (BCA) designed to detect Conditional Infectious Connectivity Structures (CICSs) that exhibit self-similar properties. Simulation results demonstrate that the BCA accurately identifies self-similar patterns, except in cases of high homogeneity in transmission abilities or shallow tree generations. Empirical analysis of Canadian COVID-19 data further confirms the robustness of these self-similar structures, even in the presence of disruptions in transmission chains, aligning with observed power-law growth. In summary, the BCA detects self-similarity in early epidemic transmission stages by identifying CICSs within transmission trees, providing critical insights for forecasting epidemic trajectories and characterizing early transmission dynamics.

Suggested Citation

  • Wang, Cheng-Hua & Wen, Tzai-Hung, 2026. "Uncovering self-similar patterns in infectious disease transmission trees: Development of a Bayesian Connectivity Algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 682(C).
    • Handle: RePEc:eee:phsmap:v:682:y:2026:i:c:s0378437125008313
    DOI: 10.1016/j.physa.2025.131179
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    References listed on IDEAS

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    1. Yuqing Long & Yanguang Chen & Yajing Li, 2023. "Multifractal scaling analyses of the spatial diffusion pattern of COVID-19 pandemic in Chinese mainland," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 10(1), pages 1-13, December.
    2. Alison K. Cheeseman & Edward R. Vrscay, 2022. "Estimating the Fractal Dimensions of Vascular Networks and Other Branching Structures: Some Words of Caution," Mathematics, MDPI, vol. 10(5), pages 1-21, March.
    3. Beare, Brendan K & Toda, Alexis Akira, 2020. "On the emergence of a power law in the distribution of COVID-19 cases," University of California at San Diego, Economics Working Paper Series qt9k5027d0, Department of Economics, UC San Diego.
    4. Sk, Tahajuddin & Biswas, Santosh & Sardar, Tridip, 2022. "The impact of a power law-induced memory effect on the SARS-CoV-2 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
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