# Epidemic Threshold in Continuous-Time Evolving Networks

## TL;DR

This paper introduces a theoretical framework to accurately compute epidemic thresholds in continuous-time evolving networks, unifying various models and overcoming limitations of previous approximation methods.

## Contribution

It presents the infection propagator approach and the weak commutation condition, enabling a unified analysis of epidemic thresholds in continuous-time network models.

## Key findings

- Provides a coherent connection between discrete and continuous time models.
- Introduces the infection propagator approach for epidemic threshold calculation.
- Unifies different network models under a single formalism.

## Abstract

Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the {\em weak commutation} condition allowing the interpretation of annealed networks, activity-driven networks, and time scale separation into one formalism. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.