Global dynamics of a class of SEIRS epidemic models in a periodic environment |
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Authors: | Yukihiko Nakata Toshikazu Kuniya |
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Institution: | Department of Pure and Applied Mathematics, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan |
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Abstract: | In this paper, we study a class of periodic SEIRS epidemic models and it is shown that the global dynamics is determined by the basic reproduction number R0 which is defined through the spectral radius of a linear integral operator. If R0<1, then the disease free periodic solution is globally asymptotically stable and if R0>1, then the disease persists. Our results really improve the results in T. Zhang, Z. Teng, On a nonautonomous SEIRS model in epidemiology Bull. Math. Biol. 69 (8) (2007) 2537-2559] 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. |
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Keywords: | SEIRS model Periodic epidemic systems Uniform persistence Extinction The basic reproduction number |
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