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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 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,本文首次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了严谨的理论稳定性分析,填补了相关理论空白,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: In the process of epidemic transmission, individual behavior plays a key role in regulating the transmission dynamics. However, existing coupled models often struggle to adequately integrate the dynamic influence of multiple realistic factors on individual behavioral decisions, or fail to fully capture the diverse complex states during the spreading process. In order to accurately capture the interaction mechanism between individual behavior and epidemic transmission, a coupled behavioral decision-making and epidemic transmission model based on a two-layer network is proposed. Based on the SIS epidemic transmission framework, individual behavior regulates the infection rate and recovery rate of the epidemic through scaling factors. Based on the framework of game theory, the model incorporates multiple real-world factors such as social pressure, behavioral implementation cost, and disease perception, and constructs dynamic rules for individual behavioral decision-making process. A bi-directional dynamic coupling between behavior and epidemic transmission is explored, thereby enabling a more precise description of the dynamic impact of behavior on spreading. Compared to existing multi-layer network models, the proposed model significantly reduces the infection level of epidemic transmission and can depict oscillatory phenomena during the spreading process. For the established nonlinear system, the stability analysis combines Lyapunov theory with potential game methods to conduct rigorous theoretical analysis of multiple equilibria, and the correctness of the theory is verified by numerical simulation. Further, a sensitivity analysis is conducted for the important parameters in the model to offer theoretical guidance for epidemic control.

       

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