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The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
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Epidemic Threshold in Continuous-Time Evolving Networks.

Eugenio Valdano1, Michele Re Fiorentin2, Chiara Poletto1

  • 1INSERM, Sorbonne Université, Institut Pierre Louis d'Epidémiologie et de Santé Publique IPLESP, F75012 Paris, France.

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|February 27, 2018
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Summary
This summary is machine-generated.

This study introduces a new theoretical framework to accurately calculate epidemic thresholds in continuous time on temporal networks. It overcomes limitations of previous approximations, offering a more reliable method for understanding disease spread dynamics.

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Area of Science:

  • Epidemiology
  • Network Science
  • Theoretical Physics

Background:

  • Current models for epidemic outbreaks on temporal networks often use approximations like time scale separation and discretization.
  • These approximations can introduce biases, limiting the accuracy of predicted critical outbreak conditions.

Purpose of the Study:

  • To develop a theoretical framework for computing the epidemic threshold in continuous time on temporal networks.
  • To provide a unified formalism that incorporates various network types and temporal dynamics.

Main Methods:

  • Utilized the infection propagator approach for continuous-time analysis.
  • Introduced the weak commutation condition to unify different network models and temporal representations.

Main Results:

  • Developed a theoretical framework to compute epidemic thresholds without relying on potentially biasing approximations.
  • The weak commutation condition successfully integrates annealed networks, activity-driven networks, and time scale separation.

Conclusions:

  • The proposed framework offers a more accurate and coherent method for analyzing epidemic dynamics on temporal networks.
  • This work bridges the gap between discrete and continuous time representations, enhancing applicability to realistic scenarios.