Critical properties of the Susceptible-Exposed-Infected model with correlated temporal disorder

TL;DR

This study investigates how long-range correlated temporal noise affects the critical behavior of the Susceptible-Exposed-Infected model, revealing a shift to an infinite-noise universality class and providing analytical and simulation insights.

Contribution

It introduces a mapping of the SEI model with temporal disorder to fractional Brownian motion, showing a change in universality class and connecting it to other models like the Domany-Kinzel automaton.

Findings

Temporal noise alters the universality class from dynamical percolation to infinite-noise.

Analytical results are supported by Monte Carlo simulations.

Active temporal Griffiths phase is difficult to observe in the long-time limit.

Abstract

In this paper we study the critical properties of the non-equilibrium phase transition of the Susceptible-Exposed-Infected model under the effects of long-range correlated time-varying environmental noise on the Bethe lattice. We show that temporal noise is perturbatively relevant changing the universality class from the (mean-field) dynamical percolation to the exotic infinite-noise universality class of the contact process model. Our analytical results are based on a mapping to the one-dimensional fractional Brownian motion with an absorbing wall and is confirmed by Monte Carlo simulations. Unlike the contact process, our theory also predicts that it is quite difficult to observe the associated active temporal Griffiths phase in the long-time limit. Finally, we also show an equivalence between the infinite-noise and the compact directed percolation universality classes by relating the SEI model in the presence of temporal disorder to the Domany-Kinzel cellular automaton in the limit of compact clusters.