On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice

TL;DR

This study determines the critical point of the stochastic SIR model on a square lattice through simulations, revealing its alignment with 2D percolation universality and providing precise epidemic thresholds.

Contribution

The paper precisely locates the critical recovery probability and infection rate for the SIR model on a lattice, linking it to percolation theory and analyzing local growth probabilities.

Findings

Critical recovery probability c_0=0.1765005(10)

Infection/recovery rate lambda_c=4.66571(3)

Net transmissibility approximately 0.5384

Abstract

By means of numerical simulations and epidemic analysis, the transition point of the stochastic, asynchronous Susceptible-Infected-Recovered (SIR) model on a square lattice is found to be c_0=0.1765005(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda_c = (1-c_0)/c_0 = 4.66571(3) and a net transmissibility of (1-c_0)/(1 + 3 c_0) = 0.538410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the 2-d percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.