Global behavior of an SEIRS epidemic model with time delays

This is a study of dynamic behavior of an SEIRS epidemic model with time delays. It is shown that disease-free equilibrium is globally stable if the reproduction number is not greater than one. When the reproduction number is greater than 1, it is proved that the disease is uniformly persistent in the population, and explicit formulae are obtained by which the eventual lower bound of the fraction of infectious individuals can be computed. Local stability of endemic equilibrium is also discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.