Permanence and extinction for a nonautonomous SEIRS epidemic model

In this paper, we study the long-time behavior of a nonautonomous SEIRS epidemic model. We obtain new sufficient conditions for the permanence (uniform persistence) and extinction of infectious population of the model. By numerical examples we show that there are cases such that our results improve the previous results obtained in [T. Zhang, Z. Teng, On a nonautonomous SEIRS model in epidemiology, Bull. Math. Bio. 69 (2007) 2537–2559]. We discuss a relation between our results and open questions proposed in the paper.