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Global dynamics of a class of SEIRS epidemic models in a periodic environment. (English) Zbl 1184.34056
Summary: We study a class of periodic SEIRS epidemic models and it is shown that the global dynamics is determined by the basic reproduction number \(R_{0}\) which is defined through the spectral radius of a linear integral operator. If \(R_{0}<1\), then the disease free periodic solution is globally asymptotically stable and if \(R_{0}>1\), then the disease persists. Our results improve the results in [T. Zhang and Z. Teng, Bull. Math. Biol. 69, No. 8, 2537–2559 (2007; Zbl 1245.34040)] for the periodic case. Moreover, from our results, we see that the eradication policy on the basis of the basic reproduction number of the time-averaged system may overestimate the infectious risk of the periodic disease. Numerical simulations which support our theoretical analysis are also given.

34C60 Qualitative investigation and simulation of ordinary differential equation models
92D30 Epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
Full Text: DOI
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