Analysis and control of epidemics in temporal networks with self-excitement and behavioral changes

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.