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

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.

9 pages, 5 figures. Accepted for publication, Physical Review E

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• Recursive contact tracing in Reed-Frost epidemic models
• A branching random-walk model of disease outbreaks and the percolation backbone
• Modelling the Spread of an Epidemic in Presence of Vaccination using Cellular Automata
• Critical behavior of the stochastic SIR model on random bond-diluted lattices
• Agent-based Monte Carlo simulations for reaction-diffusion models, population dynamics, and epidemic spreading
• Effects of lattice dilution on the non-equilibrium phase transition in the stochastic Susceptible-Infectious-Recovered model