Epidemic threshold on continuous vs. discrete time evolving networks

Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We introduce a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We validate our findings against analytical and numerical results, and provide novel mathematical interpretations of annealed networks and time scale separation. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.