Our analysis begins by considering the governing equations for the stochastic SEIR model given by Eqs. ͑1a͒-͑1c͒. We neglect the i i ͑t͒ terms in Eqs. ͑1a͒-͑1c͒ so that we are considering the deterministic SEIR system. This deterministic system has two fixed points. The first fixed point is