As a first approximation of stochastic effects, we have considered additive noise. This type of noise may result from migration into and away from the population being considered. 28 Since it is difficult to estimate fluctuating migration rates, 29 it is appropriate to treat migration as an arbitrary external noise source. Also, fluctuations in the birth rate manifest itself as additive noise. Furthermore, as we are not interested in extinction events in this article, it is not necessary to use multiplicative noise. In general, for the problem considered here, it is possible that a rare event in the tail of the noise distribution may cause one or more of the S, E, and I components of the solution to become negative. In this article, we will always assume that the noise is sufficiently small so that a solution remains positive for a long enough time to gather sufficient statistics. Even though it is difficult to accurately estimate the appropriate noise level from real data, our choices of noise intensity lie within the huge confidence intervals computed in Ref. 29 . The case for multiplicative noise will be considered in a separate paper.