Here lower case denotes the realized value of the associated capital letter random variable. In this discrete time approximation we have assumed a particular ordering of events, namely that recoveries occur first, followed by deaths from among those infected individuals who did not recover, followed by new infections. Simulation studies indicated that these assumptions, as well as other possible orderings, resulted in system dynamics that were approximately equal in expectation to deterministic solutions of the continuous time SIR model. In all forward simulations of the disease dynamic (except where noted) we assume the ''true'' underlying parameter values to be those estimated by Murray [9] , with the exception of the negative binomial overdispersion parameter k. Thus, b = 0.00218, n = 0.4, and m = 0 (no disease-related mortality). We set the overdispersion parameter to be k = 0.1, in order to produce epidemics that, without intervention, have run their course by 40 time units but such that there is variation in the size of the outbreak.