Seasonal epidemic spreading on small-world networks: Biennial outbreaks and classical discrete time crystals
arXiv:2007.00979 · doi:10.1103/PhysRevResearch.3.013124
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.
arXiv comment7+4 pages, 4+1 figures; comments welcome
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