LAW OF LARGE NUMBERS FOR THE SIRS EPIDEMIC

Abstract. We establish law of large numbers for SIRS stochastic epi-demic processes: as the population size increases the paths of SIRS epidemic processes converge to the trajectories of a two dimensional dy-namical system. If the reproductive number, R0, is greater than one then the limiting system has an interior fixed point so that the epidemic processes started with a nontrivial proportion of initially infected are endemic. We show global stability of the interior fixed point of the limiting dynamical system. 1