标题： 网络行为反馈SIR流行病模型 显示英文标题

标题： Network Behavioral-Feedback SIR Epidemic Model

摘要： 我们提出了一种网络行为反馈易感-感染-恢复（SIR）流行病模型，其中描述子种群间感染率的相互作用矩阵依赖于当前流行病状态的反馈。 该模型既捕捉了个体混合、接触频率、感染和传播倾向的异质性，也捕捉了自愿的社会隔离和自我保护措施等内生行为反应。 我们研究了平衡点的稳定性，并通过几个例子说明稳定性区域的形状如何取决于相互作用矩阵的结构，为设计有效的控制策略提供了见解。 然后我们分析了动态的瞬态行为，表明对于一类特殊的秩-1相互作用矩阵，总感染曲线总是表现出单峰行为，扩展了文献中已知的感染曲线单峰性结果，并为未来的控制应用铺平了道路。 显示英文摘要

摘要： We propose a network behavioral-feedback Susceptible-Infected-Recovered (SIR) epidemic model in which the interaction matrix describing the infection rates across subpopulations depends in feedback on the current epidemic state. This model captures both heterogeneities in individuals mixing, contact frequency, aptitude to contract and spread the infection, and endogenous behavioral responses such as voluntary social distancing and the adoption of self-protective measures. We study the stability of the equilibria and illustrate through several examples how the shape of the stability region depends on the structure of the interaction matrix, providing insights for the design of effective control strategies. We then analyze the transient behavior of the dynamics, showing that, for a special class of rank-1 interaction matrices, there always exists an aggregate infection curve that exhibits a unimodal behavior, expanding the results on the unimodality of infection curve known in the literature of epidemic models and paving the way for future control applications.