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Extinction and permanence for a pulse vaccination delayed SEIRS epidemic model

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  • Zhang, Tailei
  • Teng, Zhidong

Abstract

A delayed SEIRS epidemic model with pulse vaccination and bilinear incidence rate is investigated. Using Krasnoselskii’s fixed-point theorem, we obtain the existence of disease-free periodic solution (DFPS for short) of the delayed impulsive epidemic system. Further, using the comparison method, we prove that under the condition R∗<1, the DFPS is globally attractive, and that R∗>1 implies that the disease is permanent. Theoretical results show that the disease will be extinct if the vaccination rate is larger than θ∗ and the disease is uniformly persistent if the vaccination rate is less than θ∗. Our results indicate that a long latent period of the disease or a large pulse vaccination rate will lead to eradication of the disease.

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  • Zhang, Tailei & Teng, Zhidong, 2009. "Extinction and permanence for a pulse vaccination delayed SEIRS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2411-2425.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2411-2425
    DOI: 10.1016/j.chaos.2007.07.012
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    1. Gakkhar, Sunita & Negi, Kuldeep, 2008. "Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 626-638.
    2. Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
    3. Zhang, Tailei & Teng, Zhidong, 2008. "Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1456-1468.
    4. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
    5. Pang, Guoping & Chen, Lansun, 2007. "A delayed SIRS epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1629-1635.
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    1. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.

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