Abstract
In modelling the spread of epidemics, two levels of coupling between the epidemic process and social interactions must be considered: on the one hand, human interactions continuously evolve over time, deeply affecting the epidemic process; on the other hand, the presence of an epidemic induces adaptive behaviours in the population. The theory of adaptive temporal networks represents a powerful framework for considering both these levels of coupling and for characterizing the basic mechanisms and the impact of epidemic control measures. Within this framework, we develop a general formalism for adaptive activity-driven networks, which allows to describe several adaptive behaviours of populations exposed to epidemics, including measures implemented during the COVID-19 pandemic. We focus on the characterization of two complementary protocols for contact tracing (CT): the manual reconstruction of contacts (interview-based) and the digital contact tracing (app-based). We consider a compartmental epidemic model with manual and digital CT: the model features a phase transition between an absorbing and an active phase, a closed analytical relation for the epidemic threshold is obtained while the active phase is numerically simulated, estimating the effectiveness of CT. The results show that manual tracing is more effective than the digital procedure, even considering the intrinsic delay and limited scalability of the manual protocol. This is due to the stochastic annealed nature of manual CT, in which each node randomly recalls a fraction of its contacts, in contrast with the quenched nature of digital CT where traceable nodes belong deterministically to the fraction of the population who downloaded the app. Moreover, the better performance of manual tracing is enhanced by heterogeneity in individual behavior, i.e. by the presence of superspreaders. The intrinsic difference in contacts exploration and heterogeneity make the manual procedure dominant also in hybrid protocols, suggesting a crucial role of manual CT in any tracing strategy.
