Stochastic lattice gas model describing the dynamics of an epidemic

TL;DR

This paper models epidemic spread using a stochastic lattice gas approach, revealing a critical line of phase transition in the directed percolation class and analyzing noise effects on population oscillations.

Contribution

It introduces a novel stochastic lattice gas model for epidemic dynamics and characterizes its critical behavior and phase transitions.

Findings

Identifies a critical line separating absorbing and active phases.

Shows the epidemic onset belongs to the directed percolation universality class.

Analyzes how noise influences oscillation stability.

Abstract

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed by individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S$\to$I$\to$R$\to$S (SIRS). The open process S$\to$I$\to$R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyse the role of noise in stabilizing the oscillations.