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A non-autonomous SEIRS model with general incidence rate. (English) Zbl 1338.92133
Summary: For a non-autonomous SEIRS model with general incidence, that admits [Y. Nakata and T. Kuniya, J. Math. Anal. Appl. 363, No. 1, 230–237 (2010; Zbl 1184.34056)] 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.

92D30 Epidemiology
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