Advertisement

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)

Abstract

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.

Keywords

Globally stability Vaccine effectiveness 

Notes

Acknowledgements

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

References

  1. 1.
    World Health Organization: Immunization against diseases of public health importance (2005). http://www.who.int/mediacentre/factsheets/fs288/en/index.html/
  2. 2.
    Pei, Y., Liu, S., Chen, L., et al.: Two different vaccination strategies in an SIR epidemic model with saturated infectious force. Int. J. Biomath. 1(1), 147–160 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Li, J., Ma, Z.: Stability analysis for SIS epidemic models with vaccination and constant population size. DCDSB 4(3), 637–644 (2004)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Li, J., Yang, Y., Zhou, Y.: Global stability of an epidemic model with latent stage and vaccination. Non. Anal. Real World Appl. 12(4), 2163–2173 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Yang, W., Sun, C., Arino, J.: Global analysis for a general epidemiological model with vaccination and varying population. J. Math. Anal. Appl. 372(1), 208–223 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Watanabe, T., Kiso, M., Fukuyama, S., et al.: Characterization of H7N9 influenza A viruses isolated from humans. Nature 501(7468), 551–555 (2013)CrossRefGoogle Scholar
  7. 7.
    Gabbuti, A., Romano, L., Salinelli, P., et al.: Long-term immunogenicity of hepatitis B vaccination in a cohort of Italian healthy adolescents. Vaccine 25(16), 3129–3132 (2007)CrossRefGoogle Scholar
  8. 8.
    Li, J., Xiao, Y., Zhang, F., Yang, Y.: An algebraic approach to proving the global stability of a class of epidemic models. Non. Anal. Real World Appl. 13(5), 2006–2016 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    van den Driessche, P., Watmough, J.: Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1), 29–48 (2002)MathSciNetCrossRefGoogle Scholar
  10. 10.
    LaSalle, J.P.: The stability of dynamical systems. In: Regional Conference Series in Applied Mathematics, SIAM, Philadelphia (1976)Google Scholar

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

Personalised recommendations