By analyzing two SEIS epidemic models with fixed period of latency, one of which is with constant input, another of which is with exponent input, the essential difference between their dynamic behaviors is found. For the model with constant input, the threshold is given. When the threshold is not greater than one, the disease-free equilibrium is globally asymptotically stable. When the threshold is greater than one, the disease-free equilibrium is unstable, the endemic equilibrium is locally asymptotically stable, and the disease is uniformly persistent in the population. For the model with exponent input, the endemic equilibrium is locally asymptotically stable when the period of latency is small enough; the endemic equilibrium is unstable when the period of latency is large enough.