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Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination

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  • Zhang, Tailei

Abstract

In this paper, by applying a nonstandard finite difference scheme, we formulate a discretized SIRVS epidemic model which takes into account vaccination. Under quite weak assumptions, the threshold value conditions on permanence and extinction of disease are established. Some new threshold values in product forms R0* and R1* are obtained. We show that the disease is permanent if R0*>1, and if R1*<1, then the disease is extinct. When the model degenerates into a periodic model, a sharp threshold value R0 is obtained for permanence versus extinction of disease. In order to illustrate our analytic analysis, some numerical simulations are also included in the end.

Suggested Citation

  • Zhang, Tailei, 2015. "Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 716-729.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:716-729
    DOI: 10.1016/j.amc.2015.09.071
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    References listed on IDEAS

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    1. Li, Xiuying & Wang, Wendi, 2005. "A discrete epidemic model with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 947-958.
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    Cited by:

    1. 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.
    2. Wen, Buyu & Teng, Zhidong & Li, Zhiming, 2018. "The threshold of a periodic stochastic SIVS epidemic model with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 532-549.

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