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Current understanding of the critical outbreak condition on temporal networksrelies on approximations (time scale separation, discretization) that may biasthe results. We propose a theoretical framework to compute the epidemicthreshold in continuous time through the infection propagator approach. Weintroduce the {\em weak commutation} condition allowing the interpretation ofannealed networks, activity-driven networks, and time scale separation into oneformalism. Our work provides a coherent connection between discrete andcontinuous time representations applicable to realistic scenarios.

Epidemic Threshold in Continuous-Time Evolving Networks