  For a non-autonomous SEIRS model with general incidence, that admits [T.
Kuniya and Y. Nakata, Permanence and extinction for a nonautonomous SEIRS
epidemic model, Appl. Math. Computing 218, 9321-9331 (2012)] as a very
particular case, we obtain conditions for extinction and strong persistence of
the infectives. Our conditions are computed for several particular settings and
extend the hypothesis of several proposed non-autonomous models. Additionally
we show that our conditions are robust in the sense that they persist under
small perturbations of the parameters in some suitable family. We also present
some simulations that illustrate our results.
