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中国物理学会期刊

基于贝叶斯算法的高阶网络风险传播研究

Research on Risk Propagation of Higher-Order Networks Based on Bayesian Algorithm

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  • 随着对复杂系统的深入理解, 传统基于成对交互的网络模型在描述多体过程 (如传染病在群组中的传播) 时显现出局限性, 因此引入基于单纯复形的高阶网络成为必要. 然而, 现有高阶网络传染病模型大多假设传播概率恒定, 未能反映传播过程中因个体行为适应或环境改变导致的动态变化. 针对此问题, 本文构建了作用于二阶单纯复形上的 SIR 传染病模型. 核心创新在于提出一种基于平均场近似的贝叶斯动态更新:将网络中的局部传播事件视为近似独立的伯努利试验, 利用Beta-Binomial 共轭特性, 根据实时感染数据动态修正对一阶 (边) 及二阶 (三角形) 传播概率的后验估计. 通过在 ER 随机图上进行大量独立蒙特卡洛仿真, 并与具有相同平均传播能力的固定参数模型进行严格对比, 结果表明: (1) 贝叶斯动态模型能够敏锐捕捉疫情演化中的参数时变性, 二阶交互结构显著加速了疫情爆发并提升了感染峰值; (2) 推导出的时变基本再生数 R0(t) 解析解与仿真得到的有效再生数 R0(t) 高度吻合, 验证了理论推导的准确性. 本研究揭示了高阶交互与自适应传播概率的耦合机制, 证明了在模型中引入参数动态更新对于提高预测真实性和制定精准防控策略的重要性.

    With the deepening understanding of complex systems, traditional network models based on pairwise interactions have exhibited limitations in describing multi-body processes, such as the spread of epidemics within populations.Consequently, higher-order network representations based on simplicial complexes have become increasingly necessary. However, most existing epidemic models on higher-order networks assume constant transmission probabilities, failing to capture the dynamic changes induced by individual behavioral adaptations or environmental shifts during the spreading process. To address this issue, this paper proposes an SIR epidemic model operating on second-order simplicial complexes. The core innovation lies in a Bayesian dynamic updating mechanism based on mean-field approximation: by treating local transmission events within the network as approximately independent Bernoulli trials and leveraging the Beta-Binomial conjugate property, the model dynamically updates the posterior estimates of first-order (edge) and second-order (triangle) transmission probabilities using real-time infection data. Extensive independent Monte Carlo simulations conducted on Erdős-Rényi (ER) random graphs, alongside rigorous comparisons with fixed-parameter models possessing equivalent average transmission capabilities, demonstrate that: (1) the Bayesian dynamic model sensitively captures the time-varying nature of parameters during epidemic evolution, while the second-order interaction structure significantly accelerates the outbreak and elevates the infection peak; (2) the derived analytical solution of the time-varying basic reproduction number, R0(t), is highly consistent with the effective reproduction number obtained via simulations, thereby validating the accuracy of the theoretical derivation. This study reveals the coupling mechanism between higher-order interactions and adaptive transmission probabilities, highlighting the importance of incorporating dynamic parameter updates into models to enhance predictive realism and formulate precise prevention and control strategies.

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