Seasonal epidemic spreading on small-world networks: Biennial outbreaks and classical discrete time crystals

TL;DR

This paper models seasonal epidemic spread on small-world networks, revealing a phase transition between outbreak cycles and demonstrating that network structure and non-Markovian effects can stabilize a classical discrete time crystal, linking epidemiology and condensed matter physics.

Contribution

It introduces a mean-field model for epidemic spreading on small-world networks that uncovers a phase transition and links epidemic dynamics to discrete time crystals.

Findings

Identifies a phase transition between annual and biennial outbreaks.

Shows diverging autocorrelation time indicating a classical discrete time crystal.

Derives phase diagram from mean-field theory and numerical analysis.

Abstract

We study seasonal epidemic spreading in a susceptible-infected-removed-susceptible (SIRS) model on smallworld graphs. We derive a mean-field description that accurately captures the salient features of the model, most notably a phase transition between annual and biennial outbreaks. A numerical scaling analysis exhibits a diverging autocorrelation time in the thermodynamic limit, which confirms the presence of a classical discrete time crystalline phase. We derive the phase diagram of the model both from mean-field theory and from numerics. Our work offers new perspectives by demonstrating that small-worldness and non-Markovianity can stabilize a classical discrete time crystal, and by linking recent efforts to understand such dynamical phases of matter to the century-old problem of biennial epidemics.