Finite-size scaling of the stochastic susceptible-infected-recovered model

TL;DR

This paper investigates the critical behavior of the stochastic SIR model on a square lattice using finite-size scaling, revealing its universal properties and connection to percolation theory.

Contribution

It demonstrates that the SIR model belongs to the percolation universality class through numerical simulations and analysis of finite-size effects.

Findings

The order parameter and recovered individuals' distribution depend on infection rate.

The ratio U_P has a universal value of 1.0167(1) for square systems.

The SIR model shares critical behavior with standard percolation models.

Abstract

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same as for site and bond percolation, confirming further that the SIR model is also in the percolation class.