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. 
Jaewook Joo, Joel L. Lebowitz