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Complexity And Asymptotical Behavior Of A Sirs Epidemic Model With Proportional Impulsive Vaccination

Author

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  • GUANG-ZHAO ZENG

    (Department of Mathematics, Shaoguan University, ShaoGuan, GuangDong, 512005, China)

  • LAN-SUN CHEN

    (Department of Applied Mathematics, Dalian University of Technology, DaLian, LiaoNing, 116024, China)

Abstract

This paper considers an SIRS epidemic model with proportional impulsive vaccination, which may inherently oscillate. We study the ratio-dependent impulsive control and obtain the conditions about the basic reproductive number for which the epidemic-elimination solution is globally asymptotic. On the other hand, if the epidemic turns out to be endemic, we study numerically the influences of impulsive vaccination on the periodic oscillation of a system without impulsion and find sophisticated phenomena such as chaos in this case.

Suggested Citation

  • Guang-Zhao Zeng & Lan-Sun Chen, 2005. "Complexity And Asymptotical Behavior Of A Sirs Epidemic Model With Proportional Impulsive Vaccination," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 419-431.
    • Handle: RePEc:wsi:acsxxx:v:08:y:2005:i:04:n:s0219525905000580
    DOI: 10.1142/S0219525905000580
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    Cited by:

    1. 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.

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