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Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate

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  • Zhao, Zhong
  • Chen, Lansun
  • Song, Xinyu

Abstract

In this paper, an SEIR epidemic disease model with time delay and nonlinear incidence rate is studied, and the dynamical behavior of the model under pulse vaccination is analyzed. Using the discrete dynamical system determined by the stroboscopic map, we show that there exists an infection-free periodic solution. Further, we show that the infection-free periodic solution is globally attractive when the period of impulsive effect is less than some critical value. Using a new modelling method, we obtain a sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delay, pulse vaccination can bring different effects on the dynamic behavior of the model by numerical analysis. Our results also show the time delay is “profitless”. The main feature of this paper is to introduce time delay and impulse into the SEIR epidemic model and to give pulse vaccination strategies.

Suggested Citation

  • Zhao, Zhong & Chen, Lansun & Song, Xinyu, 2008. "Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 500-510.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:3:p:500-510
    DOI: 10.1016/j.matcom.2008.02.007
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Zhao, Zhong & Wu, Xianbin, 2014. "Nonlinear analysis of a delayed stage-structured predator–prey model with impulsive effect and environment pollution," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1262-1268.
    2. R. Rakkiyappan & V. Preethi Latha & Fathalla A. Rihan, 2019. "A Fractional-Order Model for Zika Virus Infection with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-20, November.
    3. Marek B. Trawicki, 2017. "Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity," Mathematics, MDPI, vol. 5(1), pages 1-19, January.
    4. Yu, Hengguo & Zhong, Shouming & Ye, Mao, 2009. "Dynamic analysis of an ecological model with impulsive control strategy and distributed time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 619-632.

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