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Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates

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  • Hou, Juan
  • Teng, Zhidong

Abstract

In this paper, two delayed SEIR epidemic models with continuous and impulsive vaccination and saturating incidence are investigated. The dynamical behaviors of the disease are analyzed. For continuous vaccination, we obtain a basic reproductive number R1 and prove that if R1≤1 then the disease-free equilibrium is globally attractive and if R1>1 then the disease is permanent by using the Lyapunov functional method. For impulsive vaccination, we obtain two thresholds R∗ and R∗ and prove that if R∗<1 then the disease-free periodic solution is globally attractive and if R∗>1 then the disease is permanent by using the comparison theorem of impulsive differential equation and the Lyapunov functional method. Lastly, we compared the effects of two vaccination strategies.

Suggested Citation

  • Hou, Juan & Teng, Zhidong, 2009. "Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3038-3054.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:10:p:3038-3054
    DOI: 10.1016/j.matcom.2009.02.001
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    Cited by:

    1. Chen, Shanshan & Jiang, Haijun & Li, Liang & Li, Jiarong, 2020. "Dynamical behaviors and optimal control of rumor propagation model with saturation incidence on heterogeneous networks," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Weike Zhou & Yanni Xiao & Jane Marie Heffernan, 2019. "Optimal media reporting intensity on mitigating spread of an emerging infectious disease," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-18, March.
    3. Xu, Rui, 2012. "Global dynamics of an SEIS epidemiological model with time delay describing a latent period," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 90-102.
    4. Shamsi G., N. & Ali Torabi, S. & Shakouri G., H., 2018. "An option contract for vaccine procurement using the SIR epidemic model," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1122-1140.
    5. Dai, Chuanjun & Zhao, Min & Chen, Lansun, 2012. "Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 83-97.
    6. De la Sen, M. & Alonso-Quesada, S. & Ibeas, A. & Nistal, R., 2019. "On an SEIADR epidemic model with vaccination, treatment and dead-infectious corpses removal controls," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 47-79.

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