Permanence and extinction for a nonautonomous SIRS epidemic model with time delay

In this paper, a nonautonomous SIRS epidemic model with time delay is studied. We introduce some new threshold values R∗R∗ and R∗R∗ and further obtain the disease will be permanent when R∗>1R∗>1 and the disease extinct when R∗<1R∗<1. Using the method of Liapunov functional, some sufficient conditions are derived for the global attractivity of the system. The known results are extended.