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    基于个体行为决策的流行病传播过程建模与分析

    Modeling and Analysis of Coevolution Behavioral Decision-Making and Epidemic Spreading Processes

    • 摘要: 在流行病传播过程中,个体行为对传播动力学具有关键调控作用。然而,现有耦合模型常难以充分整合多重现实因素对个体行为决策的影响,或未能充分刻画传播过程中疫情反复等多种复杂状态。基于此,本文提出一种基于双层网络的行为决策与流行病传播双向动态耦合模型。该模型以 SIS (Suspective-Infected-Suspective) 流行病传播框架为基础,令个体行为通过缩放因子调控流行病的感染率与康复率,同时以博弈论为框架,整合了社会压力、行为实施成本和疾病风险感知等多重现实因素,构建了个体行为决策的动态演化规则,实现了行为决策与传播过程的双向动态耦合。相较于现有双层网络模型,本模型显著降低了流行病传播的稳态水平,提升了流行病根除能力,并能更好地捕捉复杂动力学行为,如传播过程中的振荡现象。针对这一高度非线性耦合系统,本文结合李雅普诺夫稳定性理论与位势博弈方法,对包括无病平衡点(健康态)和地方病平衡点(非健康态)在内的多种平衡点进行理论稳定性分析,并通过数值仿真验证了理论结果的正确性。进一步的关键参数敏感性分析揭示了行为因素与流行病传播的相互作用规律,为制定更有效的流行病干预策略提供了重要的理论依据。

       

      Abstract: Individual behavior critically regulates transmission dynamics during epidemic spread. However, existing coupled models often fail to fully integrate the effects of multiple realistic factors on individual behavioral decision-making or adequately characterize complex states (e.g., epidemic resurgences) in transmission processes. To address these gaps, this study proposes a bidirectional dynamic coupling model of behavioral decision-making and epidemic spread based on a two-layer network. Built on the SIS(Suspective-Infected-Suspective) epidemic framework, the model employs scaling factors to modulate epidemic infection and recovery rates via individual behaviors. Meanwhile, integrating social pressure, behavior implementation costs, and perceived disease risks within a game-theoretic framework, dynamic evolutionary rules for individual behavioral decisions are established to achieve bidirectional dynamic coupling between behavioral decision-making and transmission processes. Compared with existing two-layer network models, the proposed model significantly reduces the steady-state level of epidemic spread, enhances epidemic eradication capacity, and better captures complex dynamical behaviors (e.g., oscillations in transmission). For this highly nonlinear coupled system, theoretical stability analysis of multiple equilibria (including disease-free equilibrium and endemic equilibrium ) is conducted by combining Lyapunov stability theory with potential game methods, and numerical simulations validate the theoretical findings. Further sensitivity analysis of key parameters reveals the interaction laws between behavioral factors and epidemic spread, providing an important theoretical basis for formulating more effective epidemic intervention strategies.

       

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