发表机构
College of Business, Jumeira University; Department of Mathematical Sciences, Delaware State University（朱美拉大学商学院; 特拉华州立大学数学科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究流行病与风险意识长期共存问题，引入建模框架，将群体意识表示为动态行为状态，其因感染率内生、因疲劳衰减，与疾病动态形成反馈回路，揭示其对流行病结构和负担的调节作用，为相关建模及公共卫生准备提供依据。
AI 中文摘要
适应性人类行为被广泛认为是流行病动态的关键决定因素，但难以以机械透明且易于分析的方式纳入流行病模型。本文引入一个建模框架，其中群体层面的意识被明确表示为一种动态行为状态，它控制个体的互动可达性，而非修改内在传播概率。意识因感染流行率内生出现，并因行为疲劳而衰减，在疾病动态和社会可达性之间产生一个封闭反馈回路。该框架表明，仅意识驱动的可达性就能产生短暂的流行病波，而流行病轨迹最终会收敛到感染与风险意识的长期共存状态。通过将行为可达性与生物传播过程分离，我们表明意识反应性和行为疲劳共同调节短暂的流行病结构和长期的地方病负担，而不改变流行病入侵阈值。这些结果确定意识驱动的可达性是流行病动态的一个基本且此前未被充分体现的组成部分，为将适应性人类行为明确纳入流行病建模提供了机制基础，并为新兴和再发传染病的公共卫生准备提供信息。
英文摘要
Human behavior shapes epidemic dynamics, yet most models represent it by rescaling transmission, conflating behavior with biology and removing the memory carried by sustained protective behavior. We develop and analyze a susceptible-infected-recovered-aware model in which prevalence-driven awareness, eroded by fatigue, moves susceptible and infectious individuals between accessible and inaccessible states rather than modifying transmission probabilities. The basic reproduction number is $\mathcal{R}_0=β/(γ+μ)$, independent of behavioral parameters, and a unique endemic equilibrium exists exactly when $\mathcal{R}_0>1$, excluding backward bifurcation. Infection and awareness are uniformly persistent whenever $\mathcal{R}_0>1$. We derive an exact decomposition of the reduction in endemic burden into susceptible withdrawal and infectious sequestration, establish the effect of each behavioral parameter, and show that the endemic state depends on awareness response and fatigue only through their ratio, with prevalence vanishing linearly as fatigue vanishes. In the instantaneous-relaxation limit, the model reduces to a transmission-modulating formulation whose endemic equilibrium is locally asymptotically stable. At finite relaxation rates, however, numerical stability and bifurcation analyses reveal a Hopf transition and self-sustained epidemic cycles without an imposed delay. Relative to the SIR benchmark, awareness lengthens transient inter-epidemic periods and slows damping rather than creating the underlying transient oscillations.
