Dynamical Behavior of an SVIR Epidemiological Model with Two Stage Characteristics of Vaccine Effectiveness and Numerical Simulation

  • Xiuchao SongEmail author
  • Miaohua Liu
  • Hao Song
  • Jinshen Ren
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1084)


An SVIR epidemiological model with two stage characteristics of vaccine effectiveness is formulated. By constructing the appropriate Lyapunov functionals, it is proved that the disease free equilibrium of the system is globally stable when the basic reproduction number is less than or equal to one, and that the unique endemic equilibrium of the system is globally stable when the basic reproduction number is greater than one.


Globally stability Vaccine effectiveness 



This paper is supported by the Research Fund of Department of Basic Sciences at Air Force Engineering University (2019107).


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Xiuchao Song
    • 1
    Email author
  • Miaohua Liu
    • 1
  • Hao Song
    • 1
  • Jinshen Ren
    • 1
  1. 1.Department of Basic SciencesAir Force Engineering UniversityXi’anChina

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