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Analysis of a delayed SIR epidemic model with pulse vaccination

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  • Gao, Shujing
  • Teng, Zhidong
  • Xie, Dehui

Abstract

In this paper, a delayed SIR epidemic model with pulse vaccination is investigated. By the comparison theorem for impulsive differential equations, we obtain that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, we show that the disease is permanent if the vaccination proportion is less than some critical value under appropriate condition. By Brouwer’s fixed-point theorem, we establish sufficient condition for the existence of positive periodic solution. Our results indicate that a large vaccination rate or a short period of pulsing is a sufficient condition for the eradication of the disease.

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  • Gao, Shujing & Teng, Zhidong & Xie, Dehui, 2009. "Analysis of a delayed SIR epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1004-1011.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:1004-1011
    DOI: 10.1016/j.chaos.2007.08.056
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    References listed on IDEAS

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    1. Gao, Shujing & Chen, Lansun, 2005. "The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1013-1023.
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    Cited by:

    1. Awawdeh, Fadi & Adawi, A. & Mustafa, Z., 2009. "Solutions of the SIR models of epidemics using HAM," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3047-3052.
    2. Alrebdi, H.I. & Steklain, Andre & Amorim, Edgard P.M. & Zotos, Euaggelos, 2023. "Thermostated Susceptible-Infected-Susceptible epidemic model," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    3. Dong, Yafang & Huo, Liang'an & Zhao, Laijun, 2022. "An improved two-layer model for rumor propagation considering time delay and event-triggered impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Imane Abouelkheir & Fadwa El Kihal & Mostafa Rachik & Ilias Elmouki, 2019. "Optimal Impulse Vaccination Approach for an SIR Control Model with Short-Term Immunity," Mathematics, MDPI, vol. 7(5), pages 1-21, May.
    5. John C. Eckalbar & Pete Tsournos & Walter L. Eckalbar, 2015. "Dynamics In An Sir Model When Vaccination Demand Follows Prior Levels Of Disease Prevalence," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 18(07n08), pages 1-27, November.

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