Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice

We investigate the time evolution and steady states of the stochastic susceptible-infected-recovered-susceptible (SIRS) epidemic model on one- and two-dimensional lattices. We compare the behavior of this system, obtained from computer simulations, with those obtained from the mean-field approximation (MFA) and pair approximation (PA). The former (latter) approximates higher-order moments in terms of first- (second-) order ones. We find that the PA gives consistently better results than the MFA. In one dimension, the improvement is even qualitative.