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

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

2010-06-10

arxiv.org/abs/1006.2129v2

Phys. Rev. E 82, 051921 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1103/PhysRevE.82.051921

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.

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