基于一类友谊距离指数偏好网络的传播动力学分析

Transmission Dynamics Analysis Based on a Class of Friendship Distance Index Preference Networks

摘要: 复杂网络上的传染病传播动力学是揭示病毒扩散规律、制定防控策略的重要理论基础。传统网络模型(如BA模型、经典加权网络模型)多未考虑空间位置与社交亲密度的耦合作用，或割裂节点度与边权关联，难以精准复现真实网络拓扑，无法准确刻画传播行为。为此，本文提出友谊距离指数(FDI)，量化地理邻近性与社会亲近度对节点连边的共同影响，构建融合空间约束与社会关联的FDI网络演化模型。基于SIR传播框架，系统分析该网络的传播动力学行为，探究关键参数对传播阈值、感染规模的影响，揭示空间和社会耦合下的传播机制。研究可为真实社交网络中的传染病防控提供理论支撑，进一步完善复杂网络传播动力学研究体系。

Abstract: The dynamics of epidemic spreading on complex networks is an important theoretical basis for revealing virus diffusion rules and formulating prevention and control strategies. Traditional network models, such as the BA model and classical weighted network models, mostly ignore the coupling of spatial location and social intimacy. Some even separate the correlation between node degree and edge weight. Thus, they cannot accurately reproduce real network topologies or describe spreading behaviors precisely. To solve this problem, this paper proposes the Friendship Distance Index (FDI). It quantifies the combined impact of geographical proximity and social closeness on node connections. We also construct an FDI network evolution model that integrates spatial constraints and social correlations. Based on the SIR spreading framework, we systematically analyze the spreading dynamics of this network. We explore how key parameters affect the epidemic threshold and infection scale, and reveal the spreading mechanism under the coupling of spatial and social factors. This research can provide theoretical support for epidemic prevention and control in real social networks. It also helps improve the research system of complex network spreading dynamics.