The complexity of interaction patterns among individuals in social systems plays a fundamental role on the inception and spreading of epidemic outbreaks. Empirical evidence has shown that the network of social interactions may co-evolve with the spread of the disease at comparable time-scales. Time-varying features have also been documented in the study of the propensity of individuals toward social activity, leading to the emergence of burstiness and temporal clustering. These temporal network dynamics are not independent of the disease evolution, whereby infected individuals could experience changes in their tendency to form connections, spontaneously or due to exogenous control policies. Neglecting these phenomena in modeling epidemics could lead to dangerous mispredictions of an outbreak and ineffective control interventions. In this paper, we propose a mathematically tractable modeling framework that relies on a limited number of parameters and encapsulates all these instances of complex phenomena through the lens of activity driven networks. Hawkes processes, Markov chains, and stability theory are leveraged to assist in the analysis of the framework and the formulation of theory-based control interventions. Our mathematical findings confirm the intuition that bursty activity patterns, typical of humans, facilitate epidemic spreading, while behavioral changes aiming at individual isolation could accelerate the eradication of epidemics. The proposed tools are demonstrated on a real-world case of influenza spreading in Italy. Overall, this work contributes new insight into the theory of temporal networks, laying the foundations for the analysis and control of spreading processes over networks with complex interaction patterns.

社会系统中个体之间交互模式的复杂性在流行病爆发的发生和扩散中起着根本性的作用。经验证据表明，社交互动网络可能会在可比较的时间尺度上与疾病的传播共同发展。时变特征也已在个人对社交活动倾向的研究中得到记录，从而导致突发性和时间性聚类的出现。这些暂时的网络动态并不独立于疾病的发展，受感染的个体可能会自发地或由于外源性控制策略而经历形成联系的趋势发生变化。在流行病建模中忽略这些现象可能会导致危险的错误预测，即爆发和无效的控制干预措施。在本文中，我们提出了一个数学上易处理的建模框架，该框架依赖于有限数量的参数，并通过活动驱动的网络封装了复杂现象的所有这些实例。利用霍克斯过程，马尔可夫链和稳定性理论来帮助分析框架和制定基于理论的控制干预措施。我们的数学发现证实了一种直觉，即典型的人类突发性活动模式促进了流行病的传播，而针对个人隔离的行为改变可能会加速消灭流行病。所建议的工具已在意大利的一次现实世界流感传播案例中得到了证明。总体而言，这项工作为时态网络理论提供了新的见解，